--- _id: '14597' abstract: - lang: eng 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." article_processing_charge: No arxiv: 1 author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Alice full_name: Marveggio, Alice id: 25647992-AA84-11E9-9D75-8427E6697425 last_name: Marveggio citation: 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 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 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. . 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. short: J.L. Fischer, A. Marveggio, ArXiv (n.d.). date_created: 2023-11-23T09:30:02Z date_published: 2022-03-31T00:00:00Z date_updated: 2023-11-30T13:25:02Z day: '31' department: - _id: JuFi doi: 10.48550/ARXIV.2203.17143 ec_funded: 1 external_id: arxiv: - '2203.17143' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2203.17143 month: '03' oa: 1 oa_version: Preprint project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: arXiv publication_status: submitted related_material: record: - id: '14587' relation: dissertation_contains status: public status: public title: Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '10547' abstract: - lang: eng 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." 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). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Katharina full_name: Hopf, Katharina last_name: Hopf - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 - first_name: Alexander full_name: Mielke, Alexander last_name: Mielke citation: 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 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 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. 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. 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. short: J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical Analysis 54 (2022) 220–267. date_created: 2021-12-16T12:08:56Z date_published: 2022-01-04T00:00:00Z date_updated: 2023-08-02T13:37:03Z day: '04' department: - _id: JuFi doi: 10.1137/20M1387237 external_id: arxiv: - '2012.03792 ' isi: - '000762768000006' intvolume: ' 54' isi: 1 issue: '1' keyword: - Energy-Reaction-Diffusion Systems - Cross Diffusion - Global-In-Time Existence of Weak/Renormalised Solutions - Entropy Method - Onsager System - Soret/Dufour Effect language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2012.03792 month: '01' oa: 1 oa_version: Preprint page: 220-267 publication: SIAM Journal on Mathematical Analysis publication_identifier: issn: - 0036-1410 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Global existence analysis of energy-reaction-diffusion systems type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 54 year: '2022' ... --- _id: '10548' abstract: - lang: eng text: "Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution operator displays fluctuations around its expectation. The recently developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting\r\nfrom a Gaussian-like coefficient field with possibly strong correlations, we establish the convergence of the rescaled commutator to a fractional Gaussian field, depending on the decay of correlations of the coefficient field, and we\r\ninvestigate the (non)degeneracy of the limit. This extends to general dimension $d\\ge1$ previous results so far limited to dimension $d=1$, and to the continuum setting with strong correlations recent results in the discrete iid case." acknowledgement: The authors thank Ivan Nourdin and Felix Otto for inspiring discussions. The work of MD is financially supported by the CNRS-Momentum program. Financial support of AG is acknowledged from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2014-2019 Grant Agreement QUANTHOM 335410). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Mitia full_name: Duerinckx, Mitia last_name: Duerinckx - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Antoine full_name: Gloria, Antoine last_name: Gloria citation: ama: Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of applied probability. 2022;32(2):1179-1209. doi:10.1214/21-AAP1705 apa: Duerinckx, M., Fischer, J. L., & Gloria, A. (2022). Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AAP1705 chicago: Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient  Fields.” Annals of Applied Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AAP1705. ieee: M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization commutator for Gaussian coefficient  fields,” Annals of applied probability, vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022. ista: Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of applied probability. 32(2), 1179–1209. mla: Duerinckx, Mitia, et al. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient  Fields.” Annals of Applied Probability, vol. 32, no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:10.1214/21-AAP1705. short: M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022) 1179–1209. date_created: 2021-12-16T12:10:16Z date_published: 2022-04-28T00:00:00Z date_updated: 2023-08-02T13:35:06Z day: '28' department: - _id: JuFi doi: 10.1214/21-AAP1705 external_id: arxiv: - '1910.04088' isi: - '000791003700011' intvolume: ' 32' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.04088 month: '04' oa: 1 oa_version: Preprint page: 1179-1209 publication: Annals of applied probability publication_identifier: issn: - 1050-5164 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Scaling limit of the homogenization commutator for Gaussian coefficient fields type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 32 year: '2022' ... --- _id: '11701' abstract: - lang: eng 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. acknowledgement: The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Mark full_name: Veraar, Mark last_name: Veraar citation: 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 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 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. 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. 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. 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. short: A. Agresti, M. Veraar, Nonlinearity 35 (2022) 4100–4210. date_created: 2022-07-31T22:01:47Z date_published: 2022-08-04T00:00:00Z date_updated: 2023-08-03T12:25:08Z day: '04' ddc: - '510' department: - _id: JuFi doi: 10.1088/1361-6544/abd613 external_id: arxiv: - '2001.00512' isi: - '000826695900001' file: - access_level: open_access checksum: 997a4bff2dfbee3321d081328c2f1e1a content_type: application/pdf creator: dernst date_created: 2022-08-01T10:39:36Z date_updated: 2022-08-01T10:39:36Z file_id: '11715' file_name: 2022_Nonlinearity_Agresti.pdf file_size: 2122096 relation: main_file success: 1 file_date_updated: 2022-08-01T10:39:36Z has_accepted_license: '1' intvolume: ' 35' isi: 1 issue: '8' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '08' oa: 1 oa_version: Published Version page: 4100-4210 publication: Nonlinearity publication_identifier: eissn: - 1361-6544 issn: - 0951-7715 publication_status: published publisher: IOP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 35 year: '2022' ... --- _id: '11842' abstract: - lang: eng text: We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier–Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With respect to the motion of the interface, we consider pure transport by the fluid flow. Along the boundary of the domain, a complete slip boundary condition for the fluid velocities and a constant ninety degree contact angle condition for the interface are assumed. In the present work, we devise for the resulting evolution problem a suitable weak solution concept based on the framework of varifolds and establish as the main result a weak-strong uniqueness principle in 2D. The proof is based on a relative entropy argument and requires a non-trivial further development of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech. Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects of the necessarily singular geometry of the evolving fluid domains, we work for simplicity in the regime of same viscosities for the two fluids. acknowledgement: The authors warmly thank their former resp. current PhD advisor Julian Fischer for the suggestion of this problem and for valuable initial discussions on the subjects of this paper. 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. article_number: '93' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Alice full_name: Marveggio, Alice id: 25647992-AA84-11E9-9D75-8427E6697425 last_name: Marveggio citation: ama: Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2 apa: Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2 chicago: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature, 2022. https://doi.org/10.1007/s00021-022-00722-2. ieee: S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities,” Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature, 2022. ista: Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 24(3), 93. mla: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature, 2022, doi:10.1007/s00021-022-00722-2. short: S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022). date_created: 2022-08-14T22:01:45Z date_published: 2022-08-01T00:00:00Z date_updated: 2023-11-30T13:25:02Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00021-022-00722-2 ec_funded: 1 external_id: arxiv: - '2112.11154' isi: - '000834834300001' file: - access_level: open_access checksum: 75c5f286300e6f0539cf57b4dba108d5 content_type: application/pdf creator: cchlebak date_created: 2022-08-16T06:55:22Z date_updated: 2022-08-16T06:55:22Z file_id: '11848' file_name: 2022_JMathFluidMech_Hensel.pdf file_size: 2045570 relation: main_file success: 1 file_date_updated: 2022-08-16T06:55:22Z has_accepted_license: '1' intvolume: ' 24' isi: 1 issue: '3' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Journal of Mathematical Fluid Mechanics publication_identifier: eissn: - 1422-6952 issn: - 1422-6928 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '14587' relation: dissertation_contains status: public scopus_import: '1' status: public title: Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 24 year: '2022' ... --- _id: '11858' abstract: - lang: eng text: "This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical spaces. In the first main result we obtain several new blow-up criteria for quasi- and semilinear stochastic evolution equations. In particular, for semilinear equations we obtain a Serrin type blow-up criterium, which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074, 2018) to the stochastic setting. Blow-up criteria can be used to prove global well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights in time play a central role in the proofs. Our second contribution is a new method to bootstrap Sobolev and Hölder regularity in time and space, which does not require smoothness of the initial data. The blow-up criteria are at the basis of these new methods. Moreover, in applications the bootstrap results can be combined with our blow-up criteria, to obtain efficient ways to prove global existence. This gives new results even in classical \U0001D43F2-settings, which we illustrate for a concrete SPDE. In future works in preparation we apply the results of the current paper to obtain global well-posedness results and regularity for several concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into a more flexible framework, where less restrictions on the nonlinearities are needed, and we are able to treat rough initial values from critical spaces. Moreover, we will obtain higher-order regularity results." acknowledgement: "The authors thank Emiel Lorist for helpful comments. The authors thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_number: '56' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Mark full_name: Veraar, Mark last_name: Veraar citation: ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 2022;22(2). doi:10.1007/s00028-022-00786-7 apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00786-7 chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” Journal of Evolution Equations. Springer Nature, 2022. https://doi.org/10.1007/s00028-022-00786-7. ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations in critical spaces part II,” Journal of Evolution Equations, vol. 22, no. 2. Springer Nature, 2022. ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 22(2), 56. mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” Journal of Evolution Equations, vol. 22, no. 2, 56, Springer Nature, 2022, doi:10.1007/s00028-022-00786-7. short: A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022). date_created: 2022-08-16T08:39:43Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-08-03T12:53:51Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00028-022-00786-7 external_id: isi: - '000809108500001' file: - access_level: open_access checksum: 59b99d1b48b6bd40983e7ce298524a21 content_type: application/pdf creator: kschuh date_created: 2022-08-16T08:52:46Z date_updated: 2022-08-16T08:52:46Z file_id: '11862' file_name: 2022_Journal of Evolution Equations_Agresti.pdf file_size: 1758371 relation: main_file success: 1 file_date_updated: 2022-08-16T08:52:46Z has_accepted_license: '1' intvolume: ' 22' isi: 1 issue: '2' keyword: - Mathematics (miscellaneous) language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Journal of Evolution Equations publication_identifier: eissn: - 1424-3202 issn: - 1424-3199 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Nonlinear parabolic stochastic evolution equations in critical spaces part II tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 22 year: '2022' ... --- _id: '12079' abstract: - lang: eng text: We extend the recent rigorous convergence result of Abels and Moser (SIAM J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin boundary condition towards evolution by mean curvature flow with constant contact angle. More precisely, in the present work we manage to remove the perturbative assumption on the contact angle being close to 90∘. We establish under usual double-well type assumptions on the potential and for a certain class of boundary energy densities the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π). For a very specific form of the boundary energy density, we even obtain from our methods a sharp convergence rate of order ε; again for general contact angles α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic expansions and stability estimates for the linearized Allen–Cahn operator. Instead, we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233, 2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy technique. We develop a careful adaptation of their approach in order to encode the constant contact angle condition. In fact, we perform this task at the level of the notion of gradient flow calibrations. This concept was recently introduced in the context of weak-strong uniqueness for multiphase mean curvature flow by Fischer et al. (arXiv:2003.05478v2). 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.\r\nOpen Access funding enabled and organized by Projekt DEAL." article_number: '201' article_processing_charge: No article_type: original author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Maximilian full_name: Moser, Maximilian id: a60047a9-da77-11eb-85b4-c4dc385ebb8c last_name: Moser citation: ama: 'Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. 2022;61(6). doi:10.1007/s00526-022-02307-3' apa: 'Hensel, S., & Moser, M. (2022). Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-022-02307-3' chicago: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2022. https://doi.org/10.1007/s00526-022-02307-3.' ieee: 'S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime,” Calculus of Variations and Partial Differential Equations, vol. 61, no. 6. Springer Nature, 2022.' ista: 'Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. 61(6), 201.' mla: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus of Variations and Partial Differential Equations, vol. 61, no. 6, 201, Springer Nature, 2022, doi:10.1007/s00526-022-02307-3.' short: S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations 61 (2022). date_created: 2022-09-11T22:01:54Z date_published: 2022-08-24T00:00:00Z date_updated: 2023-08-03T13:48:30Z day: '24' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00526-022-02307-3 ec_funded: 1 external_id: isi: - '000844247300008' file: - access_level: open_access checksum: b2da020ce50440080feedabeab5b09c4 content_type: application/pdf creator: dernst date_created: 2023-01-20T08:56:01Z date_updated: 2023-01-20T08:56:01Z file_id: '12320' file_name: 2022_Calculus_Hensel.pdf file_size: 1278493 relation: main_file success: 1 file_date_updated: 2023-01-20T08:56:01Z has_accepted_license: '1' intvolume: ' 61' isi: 1 issue: '6' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Calculus of Variations and Partial Differential Equations publication_identifier: eissn: - 1432-0835 issn: - 0944-2669 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: 'Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 61 year: '2022' ... --- _id: '8792' abstract: - lang: eng text: This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's two-scale approach. The main working assumptions are made on the behaviour of the heat flux as the absolute temperature tends to zero and to infinity. A suitable Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary value problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model is proved by deriving suitable a priori estimates and by showing weak sequential stability of families of approximating solutions. At last, some highlights are given regarding a possible approximation scheme compatible with the a-priori estimates available for the system. acknowledgement: G. Schimperna has been partially supported by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Alice full_name: Marveggio, Alice id: 25647992-AA84-11E9-9D75-8427E6697425 last_name: Marveggio - first_name: Giulio full_name: Schimperna, Giulio last_name: Schimperna citation: ama: Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 2021;274(2):924-970. doi:10.1016/j.jde.2020.10.030 apa: Marveggio, A., & Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2020.10.030 chicago: Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2020.10.030. ieee: A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based on a microforce balance,” Journal of Differential Equations, vol. 274, no. 2. Elsevier, pp. 924–970, 2021. ista: Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 274(2), 924–970. mla: Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations, vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:10.1016/j.jde.2020.10.030. short: A. Marveggio, G. Schimperna, Journal of Differential Equations 274 (2021) 924–970. date_created: 2020-11-22T23:01:26Z date_published: 2021-02-15T00:00:00Z date_updated: 2023-08-04T11:12:16Z day: '15' department: - _id: JuFi doi: 10.1016/j.jde.2020.10.030 external_id: arxiv: - '2004.02618' isi: - '000600845300023' intvolume: ' 274' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2004.02618 month: '02' oa: 1 oa_version: Preprint page: 924-970 publication: Journal of Differential Equations publication_identifier: eissn: - '10902732' issn: - '00220396' publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: On a non-isothermal Cahn-Hilliard model based on a microforce balance type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 274 year: '2021' ... --- _id: '9240' abstract: - lang: eng text: A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension . It is a regularised and inertial version of the Dean–Kawasaki model. A high-probability well-posedness theory for this model is developed. This theory improves significantly on the spatial scaling restrictions imposed in an earlier work of the same authors, which applied only to significantly larger particles in one dimension. The well-posedness theory now applies in d-dimensions when the particle-width ϵ is proportional to for and N is the number of particles. This scaling is optimal in a certain Sobolev norm. Key tools of the analysis are fractional Sobolev spaces, sharp bounds on Bessel functions, separability of the regularisation in the d-spatial dimensions, and use of the Faà di Bruno's formula. acknowledgement: All authors thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. This paper was motivated by stimulating discussions at the First Berlin–Leipzig Workshop on Fluctuating Hydrodynamics in August 2019 with Ana Djurdjevac, Rupert Klein and Ralf Kornhuber. JZ gratefully acknowledges funding by a Royal Society Wolfson Research Merit Award. FC gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Federico full_name: Cornalba, Federico id: 2CEB641C-A400-11E9-A717-D712E6697425 last_name: Cornalba - first_name: Tony full_name: Shardlow, Tony last_name: Shardlow - first_name: Johannes full_name: Zimmer, Johannes last_name: Zimmer citation: ama: Cornalba F, Shardlow T, Zimmer J. Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. 2021;284(5):253-283. doi:10.1016/j.jde.2021.02.048 apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2021). Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2021.02.048 chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “Well-Posedness for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several Space Dimensions.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2021.02.048. ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions,” Journal of Differential Equations, vol. 284, no. 5. Elsevier, pp. 253–283, 2021. ista: Cornalba F, Shardlow T, Zimmer J. 2021. Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. 284(5), 253–283. mla: Cornalba, Federico, et al. “Well-Posedness for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several Space Dimensions.” Journal of Differential Equations, vol. 284, no. 5, Elsevier, 2021, pp. 253–83, doi:10.1016/j.jde.2021.02.048. short: F. Cornalba, T. Shardlow, J. Zimmer, Journal of Differential Equations 284 (2021) 253–283. date_created: 2021-03-14T23:01:32Z date_published: 2021-05-25T00:00:00Z date_updated: 2023-08-07T14:08:05Z day: '25' ddc: - '510' department: - _id: JuFi doi: 10.1016/j.jde.2021.02.048 ec_funded: 1 external_id: isi: - '000634823300010' file: - access_level: open_access checksum: c630b691fb9e716b02aa6103a9794ec8 content_type: application/pdf creator: dernst date_created: 2021-03-22T07:18:01Z date_updated: 2021-03-22T07:18:01Z file_id: '9267' file_name: 2021_JourDiffEquations_Cornalba.pdf file_size: 473310 relation: main_file success: 1 file_date_updated: 2021-03-22T07:18:01Z has_accepted_license: '1' intvolume: ' 284' isi: 1 issue: '5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 253-283 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Differential Equations publication_identifier: eissn: - 1090-2732 issn: - 0022-0396 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 284 year: '2021' ... --- _id: '9307' abstract: - lang: eng text: We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions. acknowledgement: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem as well as helpful discussions. Special thanks go to F. Cornalba for suggesting the additional κ-truncation in Proposition 5. I am also indebted to an anonymous referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning the treatment of the noise term). The issue is resolved in this version. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 citation: ama: 'Hensel S. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 2021;9:892–939. doi:10.1007/s40072-021-00188-9' apa: 'Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-021-00188-9' chicago: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2021. https://doi.org/10.1007/s40072-021-00188-9.' ieee: 'S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation with transport noise,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 9. Springer Nature, pp. 892–939, 2021.' ista: 'Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 9, 892–939.' mla: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 9, Springer Nature, 2021, pp. 892–939, doi:10.1007/s40072-021-00188-9.' short: 'S. Hensel, Stochastics and Partial Differential Equations: Analysis and Computations 9 (2021) 892–939.' date_created: 2021-04-04T22:01:21Z date_published: 2021-03-21T00:00:00Z date_updated: 2023-08-07T14:31:59Z day: '21' ddc: - '510' department: - _id: JuFi doi: 10.1007/s40072-021-00188-9 ec_funded: 1 external_id: isi: - '000631001700001' file: - access_level: open_access checksum: 6529b609c9209861720ffa4685111bc6 content_type: application/pdf creator: dernst date_created: 2021-04-06T09:31:28Z date_updated: 2021-04-06T09:31:28Z file_id: '9309' file_name: 2021_StochPartDiffEquation_Hensel.pdf file_size: 727005 relation: main_file success: 1 file_date_updated: 2021-04-06T09:31:28Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 892–939 project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: 'Stochastics and Partial Differential Equations: Analysis and Computations' publication_identifier: eissn: - 2194-041X issn: - 2194-0401 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Finite time extinction for the 1D stochastic porous medium equation with transport noise tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ... --- _id: '9335' abstract: - lang: eng text: 'Various degenerate diffusion equations exhibit a waiting time phenomenon: depending on the “flatness” of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin film equations, and we obtain sufficient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. For the spatially discrete solution, the waiting time phenomenon refers to a deviation of the edge of support from its original position by a quantity comparable to the mesh width, over a mesh-independent time interval. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique à la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations.' acknowledgement: This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics”. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Daniel full_name: Matthes, Daniel last_name: Matthes citation: ama: Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. 2021;59(1):60-87. doi:10.1137/19M1300017 apa: Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017 chicago: Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/19M1300017. ieee: J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized porous medium and thin film equations,” SIAM Journal on Numerical Analysis, vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021. ista: Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1), 60–87. mla: Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics, 2021, pp. 60–87, doi:10.1137/19M1300017. short: J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87. date_created: 2021-04-18T22:01:42Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-08-08T13:10:40Z day: '01' department: - _id: JuFi doi: 10.1137/19M1300017 external_id: arxiv: - '1911.04185' isi: - '000625044600003' intvolume: ' 59' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1911.04185 month: '01' oa: 1 oa_version: Preprint page: 60-87 publication: SIAM Journal on Numerical Analysis publication_identifier: issn: - 0036-1429 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: The waiting time phenomenon in spatially discretized porous medium and thin film equations type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 59 year: '2021' ... --- _id: '9352' abstract: - lang: eng text: This paper provides an a priori error analysis of a localized orthogonal decomposition method for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in the form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$, $\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization. acknowledgement: 'This work was initiated while the authors enjoyed the kind hospitality of the Hausdorff Institute for Mathematics in Bonn during the trimester program Multiscale Problems: Algorithms, Numerical Analysis, and Computation. D. Peterseim would like to acknowledge the kind hospitality of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), where parts of this research were developed under the frame of the thematic program Numerical Analysis of Complex PDE Models in the Sciences.' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Dietmar full_name: Gallistl, Dietmar last_name: Gallistl - first_name: Dietmar full_name: Peterseim, Dietmar last_name: Peterseim citation: ama: Fischer JL, Gallistl D, Peterseim D. A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. 2021;59(2):660-674. doi:10.1137/19M1308992 apa: Fischer, J. L., Gallistl, D., & Peterseim, D. (2021). A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1308992 chicago: Fischer, Julian L, Dietmar Gallistl, and Dietmar Peterseim. “A Priori Error Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/19M1308992. ieee: J. L. Fischer, D. Gallistl, and D. Peterseim, “A priori error analysis of a numerical stochastic homogenization method,” SIAM Journal on Numerical Analysis, vol. 59, no. 2. Society for Industrial and Applied Mathematics, pp. 660–674, 2021. ista: Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674. mla: Fischer, Julian L., et al. “A Priori Error Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on Numerical Analysis, vol. 59, no. 2, Society for Industrial and Applied Mathematics, 2021, pp. 660–74, doi:10.1137/19M1308992. short: J.L. Fischer, D. Gallistl, D. Peterseim, SIAM Journal on Numerical Analysis 59 (2021) 660–674. date_created: 2021-04-25T22:01:31Z date_published: 2021-03-09T00:00:00Z date_updated: 2023-08-08T13:13:37Z day: '09' department: - _id: JuFi doi: 10.1137/19M1308992 external_id: arxiv: - '1912.11646' isi: - '000646030400003' intvolume: ' 59' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1912.11646 month: '03' oa: 1 oa_version: Preprint page: 660-674 publication: SIAM Journal on Numerical Analysis publication_identifier: issn: - 0036-1429 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: A priori error analysis of a numerical stochastic homogenization method type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 59 year: '2021' ... --- _id: '10005' abstract: - lang: eng text: We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations. acknowledgement: "M. Bulíček and J. Málek acknowledge the support of the project No. 18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers of the Nečas Center for Mathematical Modelling.\r\n" article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Miroslav full_name: Bulíček, Miroslav last_name: Bulíček - first_name: Erika full_name: Maringová, Erika id: dbabca31-66eb-11eb-963a-fb9c22c880b4 last_name: Maringová - first_name: Josef full_name: Málek, Josef last_name: Málek citation: ama: Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 2021;31(09). doi:10.1142/S0218202521500457 apa: Bulíček, M., Maringová, E., & Málek, J. (2021). On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. World Scientific. https://doi.org/10.1142/S0218202521500457 chicago: Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical Models and Methods in Applied Sciences. World Scientific, 2021. https://doi.org/10.1142/S0218202521500457. ieee: M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic type with implicit constitutive equations involving flux,” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 09. World Scientific, 2021. ista: Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09). mla: Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 09, World Scientific, 2021, doi:10.1142/S0218202521500457. short: M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021). date_created: 2021-09-12T22:01:25Z date_published: 2021-08-25T00:00:00Z date_updated: 2023-09-04T11:43:45Z day: '25' department: - _id: JuFi doi: 10.1142/S0218202521500457 external_id: arxiv: - '2009.06917' isi: - '000722222900004' intvolume: ' 31' isi: 1 issue: '09' keyword: - Nonlinear parabolic systems - implicit constitutive theory - weak solutions - existence - uniqueness language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2009.06917 month: '08' oa: 1 oa_version: Preprint project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Mathematical Models and Methods in Applied Sciences publication_identifier: eissn: - 1793-6314 issn: - 0218-2025 publication_status: published publisher: World Scientific quality_controlled: '1' scopus_import: '1' status: public title: On nonlinear problems of parabolic type with implicit constitutive equations involving flux type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2021' ... --- _id: '10007' abstract: - lang: eng text: The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 citation: ama: 'Hensel S. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. 2021. doi:10.15479/at:ista:10007' apa: 'Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007' chicago: 'Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10007.' ieee: 'S. Hensel, “Curvature driven interface evolution: Uniqueness properties of weak solution concepts,” Institute of Science and Technology Austria, 2021.' ista: 'Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria.' mla: 'Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10007.' short: 'S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts, Institute of Science and Technology Austria, 2021.' date_created: 2021-09-13T11:12:34Z date_published: 2021-09-14T00:00:00Z date_updated: 2023-09-07T13:30:45Z day: '14' ddc: - '515' degree_awarded: PhD department: - _id: GradSch - _id: JuFi doi: 10.15479/at:ista:10007 ec_funded: 1 file: - access_level: closed checksum: c8475faaf0b680b4971f638f1db16347 content_type: application/x-zip-compressed creator: shensel date_created: 2021-09-13T11:03:24Z date_updated: 2021-09-15T14:37:30Z file_id: '10008' file_name: thesis_final_Hensel.zip file_size: 15022154 relation: source_file - access_level: open_access checksum: 1a609937aa5275452822f45f2da17f07 content_type: application/pdf creator: shensel date_created: 2021-09-13T14:18:56Z date_updated: 2021-09-14T09:52:47Z file_id: '10014' file_name: thesis_final_Hensel.pdf file_size: 6583638 relation: main_file file_date_updated: 2021-09-15T14:37:30Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '300' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '10012' relation: part_of_dissertation status: public - id: '10013' relation: part_of_dissertation status: public - id: '7489' relation: part_of_dissertation status: public status: public supervisor: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X title: 'Curvature driven interface evolution: Uniqueness properties of weak solution concepts' type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2021' ... --- _id: '10011' abstract: - lang: eng text: We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow - is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle. 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. The content of this paper was developed and parts of it were written during a visit of the first author to the Hausdorff Center of Mathematics (HCM), University of Bonn. The hospitality and the support of HCM are gratefully acknowledged. article_number: '2109.04233' article_processing_charge: No arxiv: 1 author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Tim full_name: Laux, Tim last_name: Laux citation: ama: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness. arXiv. doi:10.48550/arXiv.2109.04233' apa: 'Hensel, S., & Laux, T. (n.d.). A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness. arXiv. https://doi.org/10.48550/arXiv.2109.04233' chicago: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of  the Allen-Cahn Equation and Weak-Strong Uniqueness.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2109.04233.' ieee: 'S. Hensel and T. Laux, “A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness,” arXiv. .' ista: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness. arXiv, 2109.04233.' mla: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of  the Allen-Cahn Equation and Weak-Strong Uniqueness.” ArXiv, 2109.04233, doi:10.48550/arXiv.2109.04233.' short: S. Hensel, T. Laux, ArXiv (n.d.). date_created: 2021-09-13T12:17:10Z date_published: 2021-09-09T00:00:00Z date_updated: 2023-05-03T10:34:38Z day: '09' department: - _id: JuFi doi: 10.48550/arXiv.2109.04233 ec_funded: 1 external_id: arxiv: - '2109.04233' keyword: - Mean curvature flow - gradient flows - varifolds - weak solutions - weak-strong uniqueness - calibrated geometry - gradient-flow calibrations language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2109.04233 month: '09' oa: 1 oa_version: Preprint project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: arXiv publication_status: submitted status: public title: 'A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness' type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '10013' abstract: - lang: eng 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 of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions. 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. article_number: '2108.01733' article_processing_charge: No arxiv: 1 author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Tim full_name: Laux, Tim last_name: Laux citation: ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv. doi:10.48550/arXiv.2108.01733 apa: Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733 chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733. ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” arXiv. . ista: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv, 2108.01733. mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733. short: S. Hensel, T. Laux, ArXiv (n.d.). date_created: 2021-09-13T12:17:11Z date_published: 2021-08-03T00:00:00Z date_updated: 2023-09-07T13:30:45Z day: '03' department: - _id: JuFi doi: 10.48550/arXiv.2108.01733 ec_funded: 1 external_id: arxiv: - '2108.01733' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2108.01733 month: '08' oa: 1 oa_version: Preprint project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: arXiv publication_status: submitted related_material: record: - id: '13043' relation: later_version status: public - id: '10007' relation: dissertation_contains status: public status: public title: Weak-strong uniqueness for the mean curvature flow of double bubbles type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '10174' abstract: - lang: eng text: Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting of monotone operators with p-growth. This first work is dedicated to a quantitative two-scale expansion result. Fluctuations will be addressed in companion articles. By treating the range of exponents 2≤p<∞ in dimensions d≤3, we are able to consider genuinely nonlinear elliptic equations and systems such as −∇⋅A(x)(1+|∇u|p−2)∇u=f (with A random, non-necessarily symmetric) for the first time. When going from p=2 to p>2, the main difficulty is to analyze the associated linearized operator, whose coefficients are degenerate, unbounded, and depend on the random input A via the solution of a nonlinear equation. One of our main achievements is the control of this intricate nonlinear dependence, leading to annealed Meyers' estimates for the linearized operator, which are key to the quantitative two-scale expansion result. acknowledgement: The authors warmly thank Mitia Duerinckx for discussions on annealed estimates, and Mathias Schäffner for pointing out that the conditions of [14] apply to ̄a in the setting of Theorem 2.2 and for discussions on regularity theory for operators with non-standard growth conditions. The authors received financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement n◦ 864066). article_number: '2104.04263' article_processing_charge: No arxiv: 1 author: - first_name: Nicolas full_name: Clozeau, Nicolas id: fea1b376-906f-11eb-847d-b2c0cf46455b last_name: Clozeau - first_name: Antoine full_name: Gloria, Antoine last_name: Gloria citation: ama: 'Clozeau N, Gloria A. Quantitative nonlinear homogenization: control of oscillations. arXiv.' apa: 'Clozeau, N., & Gloria, A. (n.d.). Quantitative nonlinear homogenization: control of oscillations. arXiv.' chicago: 'Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization: Control of Oscillations.” ArXiv, n.d.' ieee: 'N. Clozeau and A. Gloria, “Quantitative nonlinear homogenization: control of oscillations,” arXiv. .' ista: 'Clozeau N, Gloria A. Quantitative nonlinear homogenization: control of oscillations. arXiv, 2104.04263.' mla: 'Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization: Control of Oscillations.” ArXiv, 2104.04263.' short: N. Clozeau, A. Gloria, ArXiv (n.d.). date_created: 2021-10-23T10:50:55Z date_published: 2021-04-09T00:00:00Z date_updated: 2021-10-28T15:44:05Z day: '09' department: - _id: JuFi external_id: arxiv: - '2104.04263' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2104.04263 month: '04' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted status: public title: 'Quantitative nonlinear homogenization: control of oscillations' type: preprint user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 year: '2021' ... --- _id: '10549' abstract: - lang: eng text: We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \varepsilon >0, we establish homogenization error estimates of the order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \varepsilon ^\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\alpha } regularity theory is available. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Stefan full_name: Neukamm, Stefan last_name: Neukamm citation: ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9 apa: Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9 chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9. ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” Archive for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021. ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452. mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:10.1007/s00205-021-01686-9. short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452. date_created: 2021-12-16T12:12:33Z date_published: 2021-06-30T00:00:00Z date_updated: 2023-08-17T06:23:21Z day: '30' ddc: - '530' department: - _id: JuFi doi: 10.1007/s00205-021-01686-9 external_id: arxiv: - '1908.02273' isi: - '000668431200001' file: - access_level: open_access checksum: cc830b739aed83ca2e32c4e0ce266a4c content_type: application/pdf creator: cchlebak date_created: 2021-12-16T14:58:08Z date_updated: 2021-12-16T14:58:08Z file_id: '10558' file_name: 2021_ArchRatMechAnalysis_Fischer.pdf file_size: 1640121 relation: main_file success: 1 file_date_updated: 2021-12-16T14:58:08Z has_accepted_license: '1' intvolume: ' 242' isi: 1 issue: '1' keyword: - Mechanical Engineering - Mathematics (miscellaneous) - Analysis language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 343-452 publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 242 year: '2021' ... --- _id: '10575' abstract: - lang: eng text: The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting. acknowledgement: The research of A. Abbatiello is supported by Einstein Foundation, Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No. 20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Anna full_name: Abbatiello, Anna last_name: Abbatiello - first_name: Miroslav full_name: Bulíček, Miroslav last_name: Bulíček - first_name: Erika full_name: Maringová, Erika id: dbabca31-66eb-11eb-963a-fb9c22c880b4 last_name: Maringová citation: ama: Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 2021;31(11):2165-2212. doi:10.1142/S0218202521500470 apa: Abbatiello, A., Bulíček, M., & Maringová, E. (2021). On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500470 chicago: Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models and Methods in Applied Sciences. World Scientific Publishing, 2021. https://doi.org/10.1142/S0218202521500470. ieee: A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary condition for Navier-Stokes-like problems,” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212, 2021. ista: Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212. mla: Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:10.1142/S0218202521500470. short: A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212. date_created: 2021-12-26T23:01:27Z date_published: 2021-10-13T00:00:00Z date_updated: 2023-08-17T06:29:01Z day: '13' ddc: - '510' department: - _id: JuFi doi: 10.1142/S0218202521500470 external_id: arxiv: - '2009.09057' isi: - '000722309400001' file: - access_level: open_access checksum: 8c0a9396335f0b70e1f5cbfe450a987a content_type: application/pdf creator: dernst date_created: 2022-05-16T10:55:45Z date_updated: 2022-05-16T10:55:45Z file_id: '11385' file_name: 2021_MathModelsMethods_Abbatiello.pdf file_size: 795483 relation: main_file success: 1 file_date_updated: 2022-05-16T10:55:45Z has_accepted_license: '1' intvolume: ' 31' isi: 1 issue: '11' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '10' oa: 1 oa_version: Published Version page: 2165-2212 project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations publication: Mathematical Models and Methods in Applied Sciences publication_identifier: eissn: - 1793-6314 issn: - 0218-2025 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: On the dynamic slip boundary condition for Navier-Stokes-like problems tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 31 year: '2021' ... --- _id: '8697' abstract: - lang: eng text: In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 citation: ama: Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772. doi:10.1088/1361-6544/ab9728 apa: Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728 chicago: Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity. IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728. ieee: J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity, vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020. ista: Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772. mla: Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity, vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728. short: J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772. date_created: 2020-10-25T23:01:16Z date_published: 2020-11-01T00:00:00Z date_updated: 2023-08-22T10:38:38Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1088/1361-6544/ab9728 external_id: arxiv: - '1906.12245' isi: - '000576492700001' file: - access_level: open_access checksum: ed90bc6eb5f32ee6157fef7f3aabc057 content_type: application/pdf creator: cziletti date_created: 2020-10-27T12:09:57Z date_updated: 2020-10-27T12:09:57Z file_id: '8710' file_name: 2020_Nonlinearity_Fischer.pdf file_size: 1223899 relation: main_file success: 1 file_date_updated: 2020-10-27T12:09:57Z has_accepted_license: '1' intvolume: ' 33' isi: 1 issue: '11' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 5733-5772 publication: Nonlinearity publication_identifier: eissn: - '13616544' issn: - '09517715' publication_status: published publisher: IOP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 33 year: '2020' ...