[{"quality_controlled":"1","doi":"10.1007/s00440-023-01254-0","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"language":[{"iso":"eng"}],"keyword":["Troll","Norway","Fjell"],"project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"title":"Annealed quantitative estimates for the quadratic 2D-discrete random matching problem","arxiv":1,"day":"04","author":[{"full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","last_name":"Clozeau","first_name":"Nicolas"},{"full_name":"Mattesini, Francesco","first_name":"Francesco","last_name":"Mattesini"}],"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"article_processing_charge":"Yes (in subscription journal)","scopus_import":"1","publication":"Probability Theory and Related Fields","department":[{"_id":"JuFi"}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-023-01254-0"}],"date_published":"2024-01-04T00:00:00Z","ddc":["510"],"has_accepted_license":"1","publication_status":"epub_ahead","oa":1,"citation":{"ieee":"N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” Probability Theory and Related Fields. Springer Nature, 2024.","chicago":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0.","short":"N. Clozeau, F. Mattesini, Probability Theory and Related Fields (2024).","ama":"Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 2024. doi:10.1007/s00440-023-01254-0","ista":"Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields.","mla":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields, Springer Nature, 2024, doi:10.1007/s00440-023-01254-0.","apa":"Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0"},"external_id":{"arxiv":["2303.00353"]},"status":"public","date_created":"2024-01-14T23:00:57Z","oa_version":"Published Version","type":"journal_article","month":"01","abstract":[{"lang":"eng","text":"We study a random matching problem on closed compact 2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures μn and νm is quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure."}],"date_updated":"2025-08-12T12:22:41Z","_id":"14797","year":"2024","acknowledgement":"NC has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences."},{"date_updated":"2024-02-05T08:54:44Z","abstract":[{"text":"We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.","lang":"eng"}],"oa_version":"Preprint","type":"journal_article","month":"01","date_created":"2024-01-28T23:01:42Z","volume":34,"year":"2024","acknowledgement":"All authors acknowledge support of the Austrian Science Fund (FWF) through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally been supported by the FWF through grants V662, Y1292, and P35359, as well as from OeAD through the WTZ grant CZ09/2023.","_id":"14884","oa":1,"publication_status":"epub_ahead","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05151"}],"date_published":"2024-01-23T00:00:00Z","status":"public","external_id":{"arxiv":["2306.05151"]},"citation":{"apa":"Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3","mla":"Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol. 34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3.","ista":"Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2), 30.","ama":"Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 2024;34(2). doi:10.1007/s00332-023-10005-3","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","chicago":"Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3.","ieee":"E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science, vol. 34, no. 2. Springer Nature, 2024."},"intvolume":" 34","day":"23","author":[{"full_name":"Davoli, Elisa","first_name":"Elisa","last_name":"Davoli"},{"full_name":"D’Elia, Lorenza","last_name":"D’Elia","first_name":"Lorenza"},{"first_name":"Jonas","last_name":"Ingmanns","full_name":"Ingmanns, Jonas","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0"}],"title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","arxiv":1,"article_number":"30","department":[{"_id":"JuFi"}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"Journal of Nonlinear Science","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"quality_controlled":"1","doi":"10.1007/s00332-023-10005-3","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"language":[{"iso":"eng"}],"issue":"2"},{"quality_controlled":"1","doi":"10.1007/s00521-023-09033-7","publication_identifier":{"issn":["0941-0643"],"eissn":["1433-3058"]},"language":[{"iso":"eng"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"title":"Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading","arxiv":1,"day":"05","author":[{"last_name":"Cornalba","first_name":"Federico","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149","full_name":"Cornalba, Federico"},{"full_name":"Disselkamp, Constantin","first_name":"Constantin","last_name":"Disselkamp"},{"full_name":"Scassola, Davide","first_name":"Davide","last_name":"Scassola"},{"full_name":"Helf, Christopher","first_name":"Christopher","last_name":"Helf"}],"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","article_type":"original","publication":"Neural Computing and Applications","department":[{"_id":"JuFi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.1007/s00521-023-09033-7","open_access":"1"}],"date_published":"2023-10-05T00:00:00Z","oa":1,"publication_status":"epub_ahead","citation":{"short":"F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications (2023).","chicago":"Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications. Springer Nature, 2023. https://doi.org/10.1007/s00521-023-09033-7.","ieee":"F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading,” Neural Computing and Applications. Springer Nature, 2023.","apa":"Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2023). Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. Springer Nature. https://doi.org/10.1007/s00521-023-09033-7","ista":"Cornalba F, Disselkamp C, Scassola D, Helf C. 2023. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications.","mla":"Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications, Springer Nature, 2023, doi:10.1007/s00521-023-09033-7.","ama":"Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. 2023. doi:10.1007/s00521-023-09033-7"},"external_id":{"arxiv":["2203.04579"]},"status":"public","date_created":"2023-10-22T22:01:16Z","date_updated":"2023-10-31T10:58:28Z","abstract":[{"lang":"eng","text":"We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format."}],"month":"10","type":"journal_article","oa_version":"Published Version","_id":"14451","year":"2023","acknowledgement":"Open access funding provided by Università degli Studi di Trieste within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft."},{"author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149","full_name":"Cornalba, Federico","first_name":"Federico","last_name":"Cornalba"},{"last_name":"Shardlow","first_name":"Tony","full_name":"Shardlow, Tony"}],"file":[{"file_name":"2023_ESAIM_Cornalba.pdf","success":1,"creator":"dernst","file_size":1508534,"relation":"main_file","content_type":"application/pdf","checksum":"3aef1475b1882c8dec112df9a5167c39","file_id":"14560","date_updated":"2023-11-20T08:34:57Z","access_level":"open_access","date_created":"2023-11-20T08:34:57Z"}],"day":"01","title":"The regularised inertial Dean' Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"EDP Sciences","department":[{"_id":"JuFi"}],"publication":"ESAIM: Mathematical Modelling and Numerical Analysis","ec_funded":1,"scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publication_identifier":{"eissn":["2804-7214"],"issn":["2822-7840"]},"doi":"10.1051/m2an/2023077","quality_controlled":"1","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"language":[{"iso":"eng"}],"issue":"5","page":"3061-3090","abstract":[{"lang":"eng","text":"The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations around the meanfield limit for large-scale particle systems in both particle density and momentum density. We focus on the following two aspects. Firstly, we set up a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide suitable definitions of numerical fluxes at the interface of the mesh elements which are consistent with the wave-type nature of the RIDK model and grant stability of the simulations, and we quantify the rate of convergence in mean square to the continuous RIDK model. Secondly, we introduce modifications of the RIDK model in order to preserve positivity of the density (such a feature only holds in a “high-probability sense” for the original RIDK model). By means of numerical simulations, we show that the modifications lead to physically realistic and positive density profiles. In one case, subject to additional regularity constraints, we also prove positivity. Finally, we present an application of our methodology to a system of diffusing and reacting particles. Our Python code is available in open-source format."}],"date_updated":"2023-11-20T08:38:47Z","type":"journal_article","oa_version":"Published Version","month":"09","volume":57,"file_date_updated":"2023-11-20T08:34:57Z","date_created":"2023-11-19T23:00:55Z","acknowledgement":"The authors thank the anonymous referees for their careful reading of the manuscript and their\r\nvaluable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 754411 (the latter funding source covered the first part of this project).","year":"2023","_id":"14554","oa":1,"publication_status":"published","has_accepted_license":"1","ddc":["510"],"date_published":"2023-09-01T00:00:00Z","status":"public","intvolume":" 57","related_material":{"link":[{"url":"https://github.com/tonyshardlow/RIDK-FD","relation":"software"}]},"citation":{"short":"F. Cornalba, T. Shardlow, ESAIM: Mathematical Modelling and Numerical Analysis 57 (2023) 3061–3090.","chicago":"Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences, 2023. https://doi.org/10.1051/m2an/2023077.","ieee":"F. Cornalba and T. Shardlow, “The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime,” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5. EDP Sciences, pp. 3061–3090, 2023.","apa":"Cornalba, F., & Shardlow, T. (2023). The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. https://doi.org/10.1051/m2an/2023077","ista":"Cornalba F, Shardlow T. 2023. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 57(5), 3061–3090.","mla":"Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5, EDP Sciences, 2023, pp. 3061–90, doi:10.1051/m2an/2023077.","ama":"Cornalba F, Shardlow T. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 2023;57(5):3061-3090. doi:10.1051/m2an/2023077"}},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)"},"ec_funded":1,"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"JuFi"}],"title":"Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences","degree_awarded":"PhD","author":[{"full_name":"Marveggio, Alice","id":"25647992-AA84-11E9-9D75-8427E6697425","first_name":"Alice","last_name":"Marveggio"}],"day":"21","file":[{"file_name":"thesis_Marveggio.pdf","success":1,"file_size":2881100,"content_type":"application/pdf","relation":"main_file","creator":"amarvegg","file_id":"14626","date_updated":"2023-11-29T09:09:31Z","checksum":"6c7db4cc86da6cdc79f7f358dc7755d4","date_created":"2023-11-29T09:09:31Z","access_level":"open_access"},{"file_name":"Thesis_Marveggio.zip","creator":"amarvegg","file_size":10189696,"relation":"source_file","content_type":"application/zip","checksum":"52f28bdf95ec82cff39f3685f9c48e7d","file_id":"14627","date_updated":"2023-11-29T09:28:30Z","access_level":"open_access","date_created":"2023-11-29T09:10:19Z"}],"language":[{"iso":"eng"}],"project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"doi":"10.15479/at:ista:14587","publication_identifier":{"issn":["2663 - 337X"]},"_id":"14587","acknowledgement":"The research projects contained in this thesis have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819).","year":"2023","file_date_updated":"2023-11-29T09:28:30Z","date_created":"2023-11-21T11:41:05Z","page":"228","type":"dissertation","month":"11","oa_version":"Published Version","abstract":[{"text":"This thesis concerns the application of variational methods to the study of evolution problems arising in fluid mechanics and in material sciences. The main focus is on weak-strong stability properties of some curvature driven interface evolution problems, such as the two-phase Navier–Stokes flow with surface tension and multiphase mean curvature flow, and on the phase-field approximation of the latter. Furthermore, we discuss a variational approach to the study of a class of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes flow with surface tension within a bounded domain. The two fluids are immiscible and separated by a sharp interface, which intersects the boundary of the domain at a constant contact angle of ninety degree. We devise a suitable concept of varifolds solutions for the associated interface evolution problem and we establish a weak-strong uniqueness principle in case of a two dimensional ambient space. In order to focus on the boundary effects and on the singular geometry of the evolving domains, we work for simplicity in the regime of same viscosities for the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow for a suitable class of multi- well potentials and for well-prepared initial data. We even establish a rate of convergence. Our relative energy approach relies on the concept of gradient-flow calibration for branching singularities in multiphase mean curvature flow and thus enables us to overcome the limitations of other approaches. To the best of the author’s knowledge, our result is the first quantitative and unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis thesis also contains a first study of weak-strong stability for planar multiphase mean curvature flow beyond the singularity resulting from a topology change. Previous weak-strong results are indeed limited to time horizons before the first topology change of the strong solution. We consider circular topology changes and we prove weak-strong stability for BV solutions to planar multiphase mean curvature flow beyond the associated singular times by dynamically adapting the strong solutions to the weak one by means of a space-time shift.\r\nIn the context of interface evolution problems, our proofs for the main results of this thesis are based on the relative energy technique, relying on novel suitable notions of relative energy functionals, which in particular measure the interface error. Our statements follow from the resulting stability estimates for the relative energy associated to the problem.\r\nAt last, we introduce a variational approach to the study of nonlinear evolution problems. This approach hinges on the minimization of a parameter dependent family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy (WIDE) functionals. We consider a class of doubly nonlinear wave equations and establish the convergence, up to subsequences, of the associated WIDE minimizers to a solution of the target problem as the parameter goes to zero.","lang":"eng"}],"date_updated":"2023-11-30T13:25:03Z","related_material":{"record":[{"status":"public","id":"11842","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"14597","status":"public"}]},"citation":{"ieee":"A. Marveggio, “Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences,” Institute of Science and Technology Austria, 2023.","chicago":"Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587.","short":"A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science and Technology Austria, 2023.","ama":"Marveggio A. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587","mla":"Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587.","ista":"Marveggio A. 2023. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria.","apa":"Marveggio, A. (2023). Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587"},"alternative_title":["ISTA Thesis"],"status":"public","date_published":"2023-11-21T00:00:00Z","ddc":["515"],"supervisor":[{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer"}],"publication_status":"published","oa":1,"has_accepted_license":"1"},{"year":"2023","_id":"14661","page":"217-247","date_updated":"2024-01-16T12:03:05Z","abstract":[{"text":"This paper is concerned with equilibrium configurations of one-dimensional particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness results for a Γ-development of the energy with the novelty that external forces are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates and thus may model dead as well as live loads. Our result is based on a new technique for deriving compactness results which are required for calculating the first-order Γ-limit in the presence of external forces: instead of comparing a configuration of n atoms to a global minimizer of the Γ-limit, we compare the configuration to a minimizer in some subclass of functions which in some sense are \"close to\" the configuration. The paper is complemented with the study of the minimizers of the Γ-limit.","lang":"eng"}],"type":"journal_article","month":"01","oa_version":"Preprint","volume":30,"date_created":"2023-12-10T23:00:59Z","status":"public","external_id":{"isi":["001115503400013"],"arxiv":["1811.09857"]},"intvolume":" 30","citation":{"short":"M. Carioni, J.L. Fischer, A. Schlömerkemper, Journal of Convex Analysis 30 (2023) 217–247.","chicago":"Carioni, Marcello, Julian L Fischer, and Anja Schlömerkemper. “External Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis. Heldermann Verlag, 2023.","ieee":"M. Carioni, J. L. Fischer, and A. Schlömerkemper, “External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development,” Journal of Convex Analysis, vol. 30, no. 1. Heldermann Verlag, pp. 217–247, 2023.","apa":"Carioni, M., Fischer, J. L., & Schlömerkemper, A. (2023). External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. Heldermann Verlag.","ista":"Carioni M, Fischer JL, Schlömerkemper A. 2023. External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. 30(1), 217–247.","mla":"Carioni, Marcello, et al. “External Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis, vol. 30, no. 1, Heldermann Verlag, 2023, pp. 217–47.","ama":"Carioni M, Fischer JL, Schlömerkemper A. External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. 2023;30(1):217-247."},"oa":1,"publication_status":"published","date_published":"2023-01-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1811.09857","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Heldermann Verlag","department":[{"_id":"JuFi"}],"publication":"Journal of Convex Analysis","article_processing_charge":"No","scopus_import":"1","article_type":"original","author":[{"first_name":"Marcello","last_name":"Carioni","full_name":"Carioni, Marcello"},{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","last_name":"Fischer","first_name":"Julian L"},{"first_name":"Anja","last_name":"Schlömerkemper","full_name":"Schlömerkemper, Anja"}],"day":"01","arxiv":1,"title":"External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development","isi":1,"language":[{"iso":"eng"}],"issue":"1","publication_identifier":{"issn":["0944-6532"],"eissn":["2363-6394"]},"quality_controlled":"1"},{"publication_status":"published","oa":1,"date_published":"2023-02-02T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.07100","open_access":"1"}],"status":"public","external_id":{"arxiv":["2105.07100"]},"intvolume":" 131","citation":{"chicago":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis. IOS Press, 2023. https://doi.org/10.3233/asy-221775.","ieee":"M. Moser, “Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result,” Asymptotic Analysis, vol. 131, no. 3–4. IOS Press, pp. 297–383, 2023.","short":"M. Moser, Asymptotic Analysis 131 (2023) 297–383.","ama":"Moser M. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 2023;131(3-4):297-383. doi:10.3233/asy-221775","apa":"Moser, M. (2023). Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. IOS Press. https://doi.org/10.3233/asy-221775","mla":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis, vol. 131, no. 3–4, IOS Press, 2023, pp. 297–383, doi:10.3233/asy-221775.","ista":"Moser M. 2023. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 131(3–4), 297–383."},"page":"297-383","abstract":[{"text":"We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface has developed and intersects the boundary ∂ Ω. The limit problem is mean curvature flow with 90°-contact angle and we show convergence in strong norms for well-prepared initial data as long as a smooth solution to the limit problem exists. To this end we assume that the limit problem has a smooth solution on [ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued Allen–Cahn equation. In order to estimate the difference of the exact and approximate solutions with a Gronwall-type argument, a spectral estimate for the linearized Allen–Cahn operator in both cases is required. The latter will be shown in a separate paper, cf. (Moser (2021)).","lang":"eng"}],"date_updated":"2024-01-09T09:22:16Z","oa_version":"Preprint","type":"journal_article","month":"02","volume":131,"date_created":"2024-01-08T13:13:28Z","acknowledgement":"The author gratefully acknowledges support through DFG, GRK 1692 “Curvature,\r\nCycles and Cohomology” during parts of the work.","year":"2023","_id":"14755","publication_identifier":{"eissn":["1875-8576"],"issn":["0921-7134"]},"doi":"10.3233/asy-221775","quality_controlled":"1","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"issue":"3-4","author":[{"first_name":"Maximilian","last_name":"Moser","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian"}],"day":"02","title":"Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result","arxiv":1,"publisher":"IOS Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"JuFi"}],"publication":"Asymptotic Analysis","scopus_import":"1","article_processing_charge":"No","article_type":"original"},{"doi":"10.1016/j.jfa.2023.110146","quality_controlled":"1","publication_identifier":{"issn":["0022-1236"]},"keyword":["Analysis"],"isi":1,"issue":"11","language":[{"iso":"eng"}],"article_number":"110146","title":"Maximal Lp-regularity and H∞-calculus for block operator matrices and applications","arxiv":1,"author":[{"last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Hussein","first_name":"Amru","full_name":"Hussein, Amru"}],"day":"01","file":[{"access_level":"open_access","date_created":"2024-01-10T11:23:57Z","checksum":"eda98ca2aa73da91bd074baed34c2b3c","date_updated":"2024-01-10T11:23:57Z","file_id":"14789","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":1120592,"success":1,"file_name":"2023_JourFunctionalAnalysis_Agresti.pdf"}],"publication":"Journal of Functional Analysis","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_processing_charge":"Yes (in subscription journal)","scopus_import":"1","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"JuFi"}],"ddc":["510"],"date_published":"2023-12-01T00:00:00Z","publication_status":"published","oa":1,"has_accepted_license":"1","intvolume":" 285","citation":{"ieee":"A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block operator matrices and applications,” Journal of Functional Analysis, vol. 285, no. 11. Elsevier, 2023.","chicago":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110146.","short":"A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).","ama":"Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 2023;285(11). doi:10.1016/j.jfa.2023.110146","ista":"Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.","mla":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” Journal of Functional Analysis, vol. 285, no. 11, 110146, Elsevier, 2023, doi:10.1016/j.jfa.2023.110146.","apa":"Agresti, A., & Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.110146"},"external_id":{"arxiv":["2108.01962"],"isi":["001081809000001"]},"status":"public","volume":285,"file_date_updated":"2024-01-10T11:23:57Z","date_created":"2024-01-10T09:15:18Z","oa_version":"Published Version","type":"journal_article","month":"12","date_updated":"2024-01-10T11:24:56Z","abstract":[{"text":"Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.","lang":"eng"}],"_id":"14772","acknowledgement":"We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for valuable discussions. We also thank the anonymous referees for their helpful comments and suggestions, and for the very accurate reading of the manuscript.\r\nThe first author has been supported partially by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. Both authors have been supported by MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative of the Federal State of Rhineland-Palatinate, Germany.","year":"2023"},{"has_accepted_license":"1","oa":1,"publication_status":"epub_ahead","main_file_link":[{"url":"https://doi.org/10.1007/s10208-023-09613-y","open_access":"1"}],"date_published":"2023-05-30T00:00:00Z","ddc":["510"],"external_id":{"isi":["000999623100001"]},"status":"public","citation":{"chicago":"Clozeau, Nicolas, Marc Josien, Felix Otto, and Qiang Xu. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s10208-023-09613-y.","ieee":"N. Clozeau, M. Josien, F. Otto, and Q. Xu, “Bias in the representative volume element method: Periodize the ensemble instead of its realizations,” Foundations of Computational Mathematics. Springer Nature, 2023.","short":"N. Clozeau, M. Josien, F. Otto, Q. Xu, Foundations of Computational Mathematics (2023).","ama":"Clozeau N, Josien M, Otto F, Xu Q. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. 2023. doi:10.1007/s10208-023-09613-y","apa":"Clozeau, N., Josien, M., Otto, F., & Xu, Q. (2023). Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-023-09613-y","ista":"Clozeau N, Josien M, Otto F, Xu Q. 2023. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics.","mla":"Clozeau, Nicolas, et al. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics, Springer Nature, 2023, doi:10.1007/s10208-023-09613-y."},"abstract":[{"lang":"eng","text":"We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩\r\n, we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩\r\n of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function."}],"date_updated":"2023-08-02T06:12:39Z","oa_version":"Published Version","type":"journal_article","month":"05","date_created":"2023-06-11T22:00:40Z","year":"2023","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","_id":"13129","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"quality_controlled":"1","doi":"10.1007/s10208-023-09613-y","language":[{"iso":"eng"}],"isi":1,"day":"30","author":[{"full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","last_name":"Clozeau","first_name":"Nicolas"},{"last_name":"Josien","first_name":"Marc","full_name":"Josien, Marc"},{"full_name":"Otto, Felix","first_name":"Felix","last_name":"Otto"},{"first_name":"Qiang","last_name":"Xu","full_name":"Xu, Qiang"}],"title":"Bias in the representative volume element method: Periodize the ensemble instead of its realizations","department":[{"_id":"JuFi"}],"publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication":"Foundations of Computational Mathematics"},{"has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2023-09-25T00:00:00Z","ddc":["510"],"external_id":{"isi":["001019018700001"]},"status":"public","citation":{"ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038","apa":"Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038","ista":"Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 368(9), 247–300.","mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp. 247–300, doi:10.1016/j.jde.2023.05.038.","chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity,” Journal of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.","short":"A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300."},"intvolume":" 368","date_updated":"2024-01-29T11:04:41Z","abstract":[{"text":"In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.","lang":"eng"}],"oa_version":"Published Version","month":"09","type":"journal_article","page":"247-300","date_created":"2023-06-18T22:00:45Z","file_date_updated":"2024-01-29T11:03:09Z","volume":368,"year":"2023","acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 948819) Image 1. The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","_id":"13135","publication_identifier":{"issn":["0022-0396"],"eissn":["1090-2732"]},"quality_controlled":"1","doi":"10.1016/j.jde.2023.05.038","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"language":[{"iso":"eng"}],"issue":"9","isi":1,"file":[{"access_level":"open_access","date_created":"2024-01-29T11:03:09Z","checksum":"246b703b091dfe047bfc79abf0891a63","date_updated":"2024-01-29T11:03:09Z","file_id":"14895","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":834638,"success":1,"file_name":"2023_JourDifferentialEquations_Agresti.pdf"}],"day":"25","author":[{"full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962","last_name":"Agresti","first_name":"Antonio"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}],"title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity","department":[{"_id":"JuFi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","ec_funded":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication":"Journal of Differential Equations"},{"department":[{"_id":"JuFi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","publication":"Journal of Mathematical Fluid Mechanics","file":[{"success":1,"file_name":"2023_JourMathFluidMech_Bulicek.pdf","content_type":"application/pdf","relation":"main_file","file_size":845748,"creator":"dernst","date_updated":"2023-08-14T07:24:17Z","file_id":"14046","checksum":"c549cd8f0dd02ed60477a05ca045f481","date_created":"2023-08-14T07:24:17Z","access_level":"open_access"}],"day":"01","author":[{"full_name":"Bulíček, Miroslav","last_name":"Bulíček","first_name":"Miroslav"},{"full_name":"Málek, Josef","first_name":"Josef","last_name":"Málek"},{"full_name":"Maringová, Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","first_name":"Erika"}],"article_number":"72","arxiv":1,"title":"On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary","issue":"3","language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"eissn":["1422-6952"],"issn":["1422-6928"]},"quality_controlled":"1","doi":"10.1007/s00021-023-00803-w","year":"2023","acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 20-11027X financed by the Czech Science foundation (GAČR). M. Bulíček and J. Málek are members of the Nečas Center for Mathematical Modelling.\r\nOpen access publishing supported by the National Technical Library in Prague.","_id":"14042","oa_version":"Published Version","month":"08","type":"journal_article","date_updated":"2023-12-13T12:08:08Z","abstract":[{"lang":"eng","text":"Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of incompressible fluids is nowadays available not only for Navier–Stokes fluids but also for various fluid models where the relation between the Cauchy stress tensor and the symmetric part of the velocity gradient is nonlinear. The majority of such studies however concerns models where such a dependence is explicit (the stress is a function of the velocity gradient), which makes the class of studied models unduly restrictive. The same concerns boundary conditions, or more precisely the slipping mechanisms on the boundary, where the no-slip is still the most preferred condition considered in the literature. Our main objective is to develop a robust mathematical theory for unsteady internal flows of implicitly constituted incompressible fluids with implicit relations between the tangential projections of the velocity and the normal traction on the boundary. The theory covers numerous rheological models used in chemistry, biorheology, polymer and food industry as well as in geomechanics. It also includes, as special cases, nonlinear slip as well as stick–slip boundary conditions. Unlike earlier studies, the conditions characterizing admissible classes of constitutive equations are expressed by means of tools of elementary calculus. In addition, a fully constructive proof (approximation scheme) is incorporated. Finally, we focus on the question of uniqueness of such weak solutions."}],"date_created":"2023-08-13T22:01:13Z","file_date_updated":"2023-08-14T07:24:17Z","volume":25,"status":"public","external_id":{"isi":["001040354900001"],"arxiv":["2301.12834"]},"citation":{"short":"M. Bulíček, J. Málek, E. Maringová, Journal of Mathematical Fluid Mechanics 25 (2023).","chicago":"Bulíček, Miroslav, Josef Málek, and Erika Maringová. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics. Springer Nature, 2023. https://doi.org/10.1007/s00021-023-00803-w.","ieee":"M. Bulíček, J. Málek, and E. Maringová, “On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary,” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3. Springer Nature, 2023.","apa":"Bulíček, M., Málek, J., & Maringová, E. (2023). On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-023-00803-w","mla":"Bulíček, Miroslav, et al. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3, 72, Springer Nature, 2023, doi:10.1007/s00021-023-00803-w.","ista":"Bulíček M, Málek J, Maringová E. 2023. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 25(3), 72.","ama":"Bulíček M, Málek J, Maringová E. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 2023;25(3). doi:10.1007/s00021-023-00803-w"},"intvolume":" 25","has_accepted_license":"1","oa":1,"publication_status":"published","ddc":["510"],"date_published":"2023-08-01T00:00:00Z"},{"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","department":[{"_id":"JuFi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","arxiv":1,"title":"Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields","file":[{"file_id":"14052","date_updated":"2023-08-14T11:51:04Z","checksum":"f83dcaecdbd3ace862c4ed97a20e8501","date_created":"2023-08-14T11:51:04Z","access_level":"open_access","file_name":"2023_StochPartialDiffEquations_Clozeau.pdf","success":1,"file_size":1635193,"relation":"main_file","content_type":"application/pdf","creator":"dernst"}],"day":"01","author":[{"full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","last_name":"Clozeau","first_name":"Nicolas"}],"language":[{"iso":"eng"}],"isi":1,"quality_controlled":"1","doi":"10.1007/s40072-022-00254-w","publication_identifier":{"issn":["2194-0401"]},"_id":"10173","year":"2023","acknowledgement":"I would like to thank my advisor Antoine Gloria for suggesting this problem to me, as well for many interesting discussions and suggestions.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","file_date_updated":"2023-08-14T11:51:04Z","date_created":"2021-10-23T10:50:22Z","volume":11,"abstract":[{"lang":"eng","text":"We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the probability space. In this contribution, we use a parabolic approach and optimally quantify the time decay of the semigroup. For the theoretical point of view, we prove an optimal decay estimate of the gradient and flux of the corrector when spatially averaged over a scale R larger than 1. For the numerical point of view, our results provide convenient tools for the analysis of various numerical methods."}],"date_updated":"2023-08-14T11:51:47Z","month":"09","type":"journal_article","oa_version":"Published Version","page":"1254–1378","citation":{"ama":"Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 2023;11:1254–1378. doi:10.1007/s40072-022-00254-w","apa":"Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00254-w","mla":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11, Springer Nature, 2023, pp. 1254–1378, doi:10.1007/s40072-022-00254-w.","ista":"Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 11, 1254–1378.","chicago":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-022-00254-w.","ieee":"N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11. Springer Nature, pp. 1254–1378, 2023.","short":"N. Clozeau, Stochastics and Partial Differential Equations: Analysis and Computations 11 (2023) 1254–1378."},"intvolume":" 11","status":"public","external_id":{"arxiv":["2102.07452"],"isi":["000799715600001"]},"ddc":["510"],"date_published":"2023-09-01T00:00:00Z","has_accepted_license":"1","oa":1,"publication_status":"published"},{"date_updated":"2023-08-01T14:40:33Z","abstract":[{"lang":"eng","text":"The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter."}],"month":"06","oa_version":"Published Version","type":"journal_article","file_date_updated":"2023-06-19T07:33:53Z","date_created":"2021-12-16T12:15:35Z","volume":33,"year":"2023","acknowledgement":"We thank the referees for their valuable comments and suggestions. A major part of this work was carried out when B. Q. Tang visited the Institute of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged. This work was partially supported by NAWI Graz.\r\nOpen access funding provided by University of Graz.","_id":"10550","has_accepted_license":"1","oa":1,"publication_status":"published","ddc":["510"],"date_published":"2023-06-07T00:00:00Z","external_id":{"arxiv":["2109.12019"],"isi":["001002343400002"]},"status":"public","citation":{"ieee":"K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion,” Journal of Nonlinear Science, vol. 33. Springer Nature, 2023.","chicago":"Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science. Springer Nature, 2023. https://doi.org/10.1007/s00332-023-09926-w.","short":"K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023).","ama":"Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w","mla":"Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w.","ista":"Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 33, 66.","apa":"Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w"},"intvolume":" 33","file":[{"success":1,"file_name":"2023_JourNonlinearScience_Fellner.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":742315,"checksum":"f3f0f0886098e31c81116cff8183750b","date_updated":"2023-06-19T07:33:53Z","file_id":"13149","access_level":"open_access","date_created":"2023-06-19T07:33:53Z"}],"day":"07","author":[{"full_name":"Fellner, Klemens","first_name":"Klemens","last_name":"Fellner"},{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L"},{"full_name":"Kniely, Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333","last_name":"Kniely","first_name":"Michael"},{"full_name":"Tang, Bao Quoc","first_name":"Bao Quoc","last_name":"Tang"}],"arxiv":1,"title":"Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion","article_number":"66","department":[{"_id":"JuFi"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","scopus_import":"1","article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publication":"Journal of Nonlinear Science","publication_identifier":{"issn":["0938-8974"],"eissn":["1432-1467"]},"quality_controlled":"1","doi":"10.1007/s00332-023-09926-w","language":[{"iso":"eng"}],"isi":1},{"ddc":["510"],"date_published":"2023-08-04T00:00:00Z","oa":1,"publication_status":"published","has_accepted_license":"1","intvolume":" 247","citation":{"apa":"Cornalba, F., & Fischer, J. L. (2023). The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01903-7","mla":"Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive for Rational Mechanics and Analysis, vol. 247, no. 5, 76, Springer Nature, 2023, doi:10.1007/s00205-023-01903-7.","ista":"Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 247(5), 76.","ama":"Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 2023;247(5). doi:10.1007/s00205-023-01903-7","short":"F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023).","chicago":"Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01903-7.","ieee":"F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,” Archive for Rational Mechanics and Analysis, vol. 247, no. 5. Springer Nature, 2023."},"status":"public","external_id":{"isi":["001043086800001"],"arxiv":["2109.06500"]},"volume":247,"file_date_updated":"2024-01-30T12:09:34Z","date_created":"2021-12-16T12:16:03Z","abstract":[{"text":"The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles.","lang":"eng"}],"date_updated":"2024-01-30T12:10:10Z","oa_version":"Published Version","type":"journal_article","month":"08","_id":"10551","acknowledgement":"We thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science Fund (FWF).","year":"2023","doi":"10.1007/s00205-023-01903-7","quality_controlled":"1","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"isi":1,"language":[{"iso":"eng"}],"issue":"5","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"arxiv":1,"title":"The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles","article_number":"76","author":[{"first_name":"Federico","last_name":"Cornalba","full_name":"Cornalba, Federico","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149"},{"last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X"}],"file":[{"success":1,"file_name":"2023_ArchiveRationalMech_Cornalba.pdf","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":1851185,"checksum":"4529eeff170b6745a461d397ee611b5a","date_updated":"2024-01-30T12:09:34Z","file_id":"14904","access_level":"open_access","date_created":"2024-01-30T12:09:34Z"}],"day":"04","publication":"Archive for Rational Mechanics and Analysis","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"scopus_import":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"JuFi"}]},{"scopus_import":"1","article_processing_charge":"No","tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"article_type":"original","publication":"Mathematische Nachrichten","department":[{"_id":"JuFi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Wiley","arxiv":1,"title":"On the trace embedding and its applications to evolution equations","file":[{"access_level":"open_access","date_created":"2023-08-16T11:40:02Z","checksum":"6f099f1d064173784d1a27716a2cc795","file_id":"14067","date_updated":"2023-08-16T11:40:02Z","creator":"dernst","file_size":449280,"content_type":"application/pdf","relation":"main_file","file_name":"2023_MathNachrichten_Agresti.pdf","success":1}],"day":"01","author":[{"full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","first_name":"Antonio"},{"first_name":"Nick","last_name":"Lindemulder","full_name":"Lindemulder, Nick"},{"first_name":"Mark","last_name":"Veraar","full_name":"Veraar, Mark"}],"language":[{"iso":"eng"}],"issue":"4","isi":1,"quality_controlled":"1","doi":"10.1002/mana.202100192","publication_identifier":{"issn":["0025-584X"],"eissn":["1522-2616"]},"_id":"12429","year":"2023","acknowledgement":"The first author has been partially supported by the Nachwuchsring—Network for the promotion of young scientists—at TU Kaiserslautern. The second and third authors were supported by the Vidi subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).","date_created":"2023-01-29T23:00:59Z","file_date_updated":"2023-08-16T11:40:02Z","volume":296,"date_updated":"2023-08-16T11:41:42Z","abstract":[{"lang":"eng","text":"In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equations, where uniform trace estimates on the half-line are shown."}],"month":"04","oa_version":"Published Version","type":"journal_article","page":"1319-1350","citation":{"apa":"Agresti, A., Lindemulder, N., & Veraar, M. (2023). On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. Wiley. https://doi.org/10.1002/mana.202100192","ista":"Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350.","mla":"Agresti, Antonio, et al. “On the Trace Embedding and Its Applications to Evolution Equations.” Mathematische Nachrichten, vol. 296, no. 4, Wiley, 2023, pp. 1319–50, doi:10.1002/mana.202100192.","ama":"Agresti A, Lindemulder N, Veraar M. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 2023;296(4):1319-1350. doi:10.1002/mana.202100192","short":"A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023) 1319–1350.","chicago":"Agresti, Antonio, Nick Lindemulder, and Mark Veraar. “On the Trace Embedding and Its Applications to Evolution Equations.” Mathematische Nachrichten. Wiley, 2023. https://doi.org/10.1002/mana.202100192.","ieee":"A. Agresti, N. Lindemulder, and M. Veraar, “On the trace embedding and its applications to evolution equations,” Mathematische Nachrichten, vol. 296, no. 4. Wiley, pp. 1319–1350, 2023."},"intvolume":" 296","external_id":{"isi":["000914134900001"],"arxiv":["2104.05063"]},"status":"public","date_published":"2023-04-01T00:00:00Z","ddc":["510"],"has_accepted_license":"1","oa":1,"publication_status":"published"},{"_id":"12486","acknowledgement":"The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti for her support in creating the picture. The author\r\nthanks the anonymous referee for helpful comments. ","year":"2023","date_created":"2023-02-02T10:45:47Z","abstract":[{"lang":"eng","text":"This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas."}],"date_updated":"2023-12-18T07:53:45Z","oa_version":"Submitted Version","month":"11","type":"journal_article","citation":{"ama":"Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. 2023. doi:10.1007/s40072-023-00319-4","mla":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations, Springer Nature, 2023, doi:10.1007/s40072-023-00319-4.","ista":"Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations.","apa":"Agresti, A. (2023). Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-023-00319-4","ieee":"A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations,” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023.","chicago":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-023-00319-4.","short":"A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations (2023)."},"external_id":{"arxiv":["2207.08293"]},"status":"public","date_published":"2023-11-28T00:00:00Z","ddc":["510"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s40072-023-00319-4"}],"publication_status":"epub_ahead","oa":1,"has_accepted_license":"1","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"JuFi"}],"title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations","arxiv":1,"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","last_name":"Agresti","first_name":"Antonio"}],"day":"28","language":[{"iso":"eng"}],"project":[{"grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials"}],"doi":"10.1007/s40072-023-00319-4","publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]}},{"has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2023-04-20T00:00:00Z","ddc":["510"],"external_id":{"arxiv":["2108.01733"],"isi":["000975817300002"]},"status":"public","citation":{"apa":"Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484","ista":"Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107.","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1, EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484.","ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484","short":"S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107.","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023. https://doi.org/10.4171/IFB/484.","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS Press, pp. 37–107, 2023."},"related_material":{"record":[{"status":"public","id":"10013","relation":"earlier_version"}]},"intvolume":" 25","oa_version":"Published Version","type":"journal_article","month":"04","abstract":[{"text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction\r\nof a gradient flow calibration in the sense of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting along triple junctions.","lang":"eng"}],"date_updated":"2023-08-01T14:43:29Z","page":"37-107","date_created":"2023-05-21T22:01:06Z","file_date_updated":"2023-05-22T07:24:13Z","volume":25,"year":"2023","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","_id":"13043","publication_identifier":{"eissn":["1463-9971"],"issn":["1463-9963"]},"quality_controlled":"1","doi":"10.4171/IFB/484","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"issue":"1","language":[{"iso":"eng"}],"isi":1,"day":"20","file":[{"access_level":"open_access","date_created":"2023-05-22T07:24:13Z","checksum":"622422484810441e48f613e968c7e7a4","date_updated":"2023-05-22T07:24:13Z","file_id":"13045","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":867876,"success":1,"file_name":"2023_Interfaces_Hensel.pdf"}],"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","first_name":"Sebastian","last_name":"Hensel"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"}],"arxiv":1,"title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","department":[{"_id":"JuFi"}],"publisher":"EMS Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","article_processing_charge":"No","scopus_import":"1","ec_funded":1,"publication":"Interfaces and Free Boundaries"},{"publication":"Nonlinearity","tmp":{"short":"CC BY (3.0)","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","image":"/images/cc_by.png"},"article_type":"original","article_processing_charge":"No","scopus_import":"1","publisher":"IOP Publishing","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"JuFi"}],"arxiv":1,"title":"Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence","author":[{"full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","first_name":"Antonio"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}],"day":"04","file":[{"creator":"dernst","file_size":2122096,"content_type":"application/pdf","relation":"main_file","file_name":"2022_Nonlinearity_Agresti.pdf","success":1,"access_level":"open_access","date_created":"2022-08-01T10:39:36Z","checksum":"997a4bff2dfbee3321d081328c2f1e1a","file_id":"11715","date_updated":"2022-08-01T10:39:36Z"}],"isi":1,"issue":"8","language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/abd613","quality_controlled":"1","publication_identifier":{"eissn":["1361-6544"],"issn":["0951-7715"]},"_id":"11701","acknowledgement":"The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).","year":"2022","volume":35,"date_created":"2022-07-31T22:01:47Z","file_date_updated":"2022-08-01T10:39:36Z","page":"4100-4210","type":"journal_article","oa_version":"Published Version","month":"08","date_updated":"2023-08-03T12:25:08Z","abstract":[{"text":"In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local existence and well-posedness. A second part in preparation is on blow-up criteria and regularization. Our theory is formulated in an Lp-setting, and because of this we can deal with nonlinearities in a very efficient way. Applications to several concrete problems and their quasilinear variants are given. This includes Burgers' equation, the Allen–Cahn equation, the Cahn–Hilliard equation, reaction–diffusion equations, and the porous media equation. The interplay of the nonlinearities and the critical spaces of initial data leads to new results and insights for these SPDEs. The proofs are based on recent developments in maximal regularity theory for the linearized problem for deterministic and stochastic evolution equations. In particular, our theory can be seen as a stochastic version of the theory of critical spaces due to Prüss–Simonett–Wilke (2018). Sharp weighted time-regularity allow us to deal with rough initial values and obtain instantaneous regularization results. The abstract well-posedness results are obtained by a combination of several sophisticated splitting and truncation arguments.","lang":"eng"}],"intvolume":" 35","citation":{"short":"A. Agresti, M. Veraar, Nonlinearity 35 (2022) 4100–4210.","ieee":"A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence,” Nonlinearity, vol. 35, no. 8. IOP Publishing, pp. 4100–4210, 2022.","chicago":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.” Nonlinearity. IOP Publishing, 2022. https://doi.org/10.1088/1361-6544/abd613.","mla":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.” Nonlinearity, vol. 35, no. 8, IOP Publishing, 2022, pp. 4100–210, doi:10.1088/1361-6544/abd613.","ista":"Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity. 35(8), 4100–4210.","apa":"Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/abd613","ama":"Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity. 2022;35(8):4100-4210. doi:10.1088/1361-6544/abd613"},"status":"public","external_id":{"arxiv":["2001.00512"],"isi":["000826695900001"]},"ddc":["510"],"date_published":"2022-08-04T00:00:00Z","oa":1,"publication_status":"published","has_accepted_license":"1"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2203.17143"}],"date_published":"2022-03-31T00:00:00Z","doi":"10.48550/ARXIV.2203.17143","oa":1,"publication_status":"submitted","language":[{"iso":"eng"}],"citation":{"apa":"Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. https://doi.org/10.48550/ARXIV.2203.17143","ista":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv, 10.48550/ARXIV.2203.17143.","mla":"Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, doi:10.48550/ARXIV.2203.17143.","ama":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143","short":"J.L. Fischer, A. Marveggio, ArXiv (n.d.).","chicago":"Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2203.17143.","ieee":"J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. ."},"related_material":{"record":[{"relation":"dissertation_contains","id":"14587","status":"public"}]},"external_id":{"arxiv":["2203.17143"]},"status":"public","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"date_created":"2023-11-23T09:30:02Z","title":"Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow","arxiv":1,"date_updated":"2023-11-30T13:25:02Z","abstract":[{"text":"Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: As long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen-Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the gradient flow structure of the Allen-Cahn equation and its limiting motion: Building on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn operator or additional convergence hypotheses for the energy at positive times.","lang":"eng"}],"day":"31","oa_version":"Preprint","type":"preprint","month":"03","author":[{"first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alice","last_name":"Marveggio","full_name":"Marveggio, Alice","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"ec_funded":1,"article_processing_charge":"No","publication":"arXiv","_id":"14597","year":"2022","department":[{"_id":"JuFi"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"external_id":{"arxiv":["2012.03792 "],"isi":["000762768000006"]},"status":"public","citation":{"apa":"Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237","mla":"Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237.","ista":"Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1), 220–267.","ama":"Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237","short":"J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical Analysis 54 (2022) 220–267.","chicago":"Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/20M1387237.","ieee":"J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022."},"intvolume":" 54","publication_status":"published","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.03792"}],"date_published":"2022-01-04T00:00:00Z","year":"2022","acknowledgement":"M.K. gratefully acknowledges the hospitality of WIAS Berlin, where a major part of the project was carried out. The research stay of M.K. at WIAS Berlin was funded by the Austrian Federal Ministry of Education, Science and Research through a research fellowship for graduates of a promotio sub auspiciis. The research of A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems” (Project no. 235221301), Subproject C05 “Effective models for materials and interfaces with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin Schrödinger Institute in Vienna, where some ideas for this work have been developed. The authors are grateful to two anonymous referees for several helpful comments, in particular for the short proof of estimate (2.7).","_id":"10547","abstract":[{"text":"We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities,\r\nwhile at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear.","lang":"eng"}],"date_updated":"2023-08-02T13:37:03Z","type":"journal_article","month":"01","oa_version":"Preprint","page":"220-267","date_created":"2021-12-16T12:08:56Z","volume":54,"language":[{"iso":"eng"}],"issue":"1","isi":1,"keyword":["Energy-Reaction-Diffusion Systems","Cross Diffusion","Global-In-Time Existence of Weak/Renormalised Solutions","Entropy Method","Onsager System","Soret/Dufour Effect"],"publication_identifier":{"issn":["0036-1410"]},"quality_controlled":"1","doi":"10.1137/20M1387237","department":[{"_id":"JuFi"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Society for Industrial and Applied Mathematics","article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"SIAM Journal on Mathematical Analysis","day":"04","author":[{"first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"full_name":"Hopf, Katharina","first_name":"Katharina","last_name":"Hopf"},{"last_name":"Kniely","first_name":"Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael"},{"full_name":"Mielke, Alexander","last_name":"Mielke","first_name":"Alexander"}],"arxiv":1,"title":"Global existence analysis of energy-reaction-diffusion systems"}]