[{"scopus_import":"1","issue":"4","arxiv":1,"citation":{"chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>.","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022.","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","apa":"Forkert, D. L., Maas, J., &#38; Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>","ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(4):4297-4333. doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>"},"project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","external_id":{"arxiv":["2008.10962"],"isi":["000889274600001"]},"related_material":{"record":[{"relation":"earlier_version","id":"10022","status":"public"}]},"publication":"SIAM Journal on Mathematical Analysis","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2008.10962","open_access":"1"}],"status":"public","date_updated":"2023-08-03T12:37:21Z","abstract":[{"text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.","lang":"eng"}],"ec_funded":1,"day":"18","page":"4297-4333","oa_version":"Preprint","publication_status":"published","intvolume":"        54","keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"JaMa"}],"acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","date_created":"2022-08-07T22:01:59Z","volume":54,"article_type":"original","isi":1,"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"quality_controlled":"1","month":"07","type":"journal_article","year":"2022","publisher":"Society for Industrial and Applied Mathematics","doi":"10.1137/21M1410968","language":[{"iso":"eng"}],"date_published":"2022-07-18T00:00:00Z","_id":"11739","oa":1,"author":[{"id":"35C79D68-F248-11E8-B48F-1D18A9856A87","last_name":"Forkert","first_name":"Dominik L","full_name":"Forkert, Dominik L"},{"full_name":"Maas, Jan","first_name":"Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Lorenzo","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale"}]},{"publication_identifier":{"issn":["0036-1410"]},"quality_controlled":"1","month":"01","article_type":"original","volume":54,"isi":1,"department":[{"_id":"JuFi"}],"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).","date_created":"2021-12-16T12:08:56Z","intvolume":"        54","keyword":["Energy-Reaction-Diffusion Systems","Cross Diffusion","Global-In-Time Existence of Weak/Renormalised Solutions","Entropy Method","Onsager System","Soret/Dufour Effect"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","_id":"10547","oa":1,"author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","first_name":"Julian L"},{"last_name":"Hopf","full_name":"Hopf, Katharina","first_name":"Katharina"},{"first_name":"Michael","full_name":"Kniely, Michael","last_name":"Kniely","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333"},{"first_name":"Alexander","full_name":"Mielke, Alexander","last_name":"Mielke"}],"date_published":"2022-01-04T00:00:00Z","year":"2022","publisher":"Society for Industrial and Applied Mathematics","doi":"10.1137/20M1387237","language":[{"iso":"eng"}],"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.03792"}],"title":"Global existence analysis of energy-reaction-diffusion systems","external_id":{"isi":["000762768000006"],"arxiv":["2012.03792 "]},"publication":"SIAM Journal on Mathematical Analysis","citation":{"mla":"Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:<a href=\"https://doi.org/10.1137/20M1387237\">10.1137/20M1387237</a>.","apa":"Fischer, J. L., Hopf, K., Kniely, M., &#38; Mielke, A. (2022). Global existence analysis of energy-reaction-diffusion systems. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/20M1387237\">https://doi.org/10.1137/20M1387237</a>","short":"J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical Analysis 54 (2022) 220–267.","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. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(1):220-267. doi:<a href=\"https://doi.org/10.1137/20M1387237\">10.1137/20M1387237</a>","chicago":"Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/20M1387237\">https://doi.org/10.1137/20M1387237</a>.","ieee":"J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis of energy-reaction-diffusion systems,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022."},"arxiv":1,"scopus_import":"1","issue":"1","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."}],"day":"04","page":"220-267","publication_status":"published","oa_version":"Preprint","date_updated":"2023-08-02T13:37:03Z","status":"public"},{"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2105.08434"}],"publication":"SIAM Journal on Mathematical Analysis","external_id":{"isi":["000762768000004"],"arxiv":["2105.08434"]},"title":"Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°","arxiv":1,"citation":{"ama":"Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(1):114-172. doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>","apa":"Abels, H., &#38; Moser, M. (2022). Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>","short":"H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.","mla":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>.","ista":"Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. 54(1), 114–172.","ieee":"H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 114–172, 2022.","chicago":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>."},"issue":"1","scopus_import":"1","page":"114-172","oa_version":"Preprint","publication_status":"published","day":"04","abstract":[{"lang":"eng","text":"This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument."}],"date_updated":"2023-08-04T10:34:56Z","status":"public","month":"01","quality_controlled":"1","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"isi":1,"article_type":"original","volume":54,"date_created":"2023-01-16T10:07:00Z","department":[{"_id":"JuFi"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"intvolume":"        54","author":[{"first_name":"Helmut","full_name":"Abels, Helmut","last_name":"Abels"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","full_name":"Moser, Maximilian","first_name":"Maximilian"}],"oa":1,"_id":"12305","date_published":"2022-01-04T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1137/21m1424925","publisher":"Society for Industrial and Applied Mathematics","year":"2022","type":"journal_article"},{"publication":"SIAM Journal on Mathematical Analysis","external_id":{"arxiv":["1904.08647 "],"isi":["000546967700022"]},"related_material":{"record":[{"relation":"dissertation_contains","id":"9733","status":"public"}]},"title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball","main_file_link":[{"url":"https://arxiv.org/abs/1904.08647","open_access":"1"}],"issue":"1","scopus_import":"1","has_accepted_license":"1","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"citation":{"ista":"Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622.","mla":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics , 2020, pp. 605–22, doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>.","short":"D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622.","apa":"Feliciangeli, D., &#38; Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics . <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>","ama":"Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(1):605-622. doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>","chicago":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics , 2020. <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>.","ieee":"D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics , pp. 605–622, 2020."},"arxiv":1,"oa_version":"Preprint","page":"605-622","publication_status":"published","day":"12","tmp":{"image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"ec_funded":1,"abstract":[{"lang":"eng","text":"We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum."}],"status":"public","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","date_updated":"2023-09-07T13:30:11Z","isi":1,"volume":52,"article_type":"original","month":"02","quality_controlled":"1","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"intvolume":"        52","date_created":"2021-08-06T07:34:16Z","department":[{"_id":"RoSe"}],"acknowledgement":"We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227.","date_published":"2020-02-12T00:00:00Z","author":[{"orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","full_name":"Feliciangeli, Dario"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"_id":"9781","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1137/19m126284x","publisher":"Society for Industrial & Applied Mathematics ","year":"2020"}]