Mielke, Alexander Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems. (English) Zbl 07783349 J. Math. Phys. 64, No. 12, Article ID 123502, 27 p. (2023). MSC: 82C35 82C31 PDFBibTeX XMLCite \textit{A. Mielke}, J. Math. Phys. 64, No. 12, Article ID 123502, 27 p. (2023; Zbl 07783349) Full Text: DOI arXiv
Gao, Yuan; Zhou, Yufan Hamilton dynamics in chemical reactions: the Maupertuis principle, transition paths and energy landscape. (English) Zbl 07747628 Commun. Math. Anal. Appl. 2, No. 3, 245-288 (2023). MSC: 49L99 80A30 49N99 PDFBibTeX XMLCite \textit{Y. Gao} and \textit{Y. Zhou}, Commun. Math. Anal. Appl. 2, No. 3, 245--288 (2023; Zbl 07747628) Full Text: DOI
Peletier, Mark A.; Renger, D. R. Michiel Fast reaction limits via \(\Gamma\)-convergence of the flux rate functional. (English) Zbl 1523.35271 J. Dyn. Differ. Equations 35, No. 1, 865-906 (2023). MSC: 35R02 35R06 35B25 PDFBibTeX XMLCite \textit{M. A. Peletier} and \textit{D. R. M. Renger}, J. Dyn. Differ. Equations 35, No. 1, 865--906 (2023; Zbl 1523.35271) Full Text: DOI arXiv
Hoeksema, Jasper; Tse, Oliver Generalized gradient structures for measure-valued population dynamics and their large-population limit. (English) Zbl 1517.35007 Calc. Var. Partial Differ. Equ. 62, No. 5, Paper No. 158, 72 p. (2023). MSC: 35A15 49J27 49J45 60K35 60J80 PDFBibTeX XMLCite \textit{J. Hoeksema} and \textit{O. Tse}, Calc. Var. Partial Differ. Equ. 62, No. 5, Paper No. 158, 72 p. (2023; Zbl 1517.35007) Full Text: DOI arXiv
Peletier, Mark A.; Schlichting, André Cosh gradient systems and tilting. (English) Zbl 1512.35003 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 231, Article ID 113094, 113 p. (2023). MSC: 35-02 35A15 35K90 35Q49 35Q84 47J35 PDFBibTeX XMLCite \textit{M. A. Peletier} and \textit{A. Schlichting}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 231, Article ID 113094, 113 p. (2023; Zbl 1512.35003) Full Text: DOI arXiv
Schmeller, Leonie; Peschka, Dirk Gradient flows for coupling order parameters and mechanics. (English) Zbl 1523.74086 SIAM J. Appl. Math. 83, No. 1, 225-253 (2023). MSC: 74N20 74B20 74S05 74S20 PDFBibTeX XMLCite \textit{L. Schmeller} and \textit{D. Peschka}, SIAM J. Appl. Math. 83, No. 1, 225--253 (2023; Zbl 1523.74086) Full Text: DOI
Gao, Yuan; Liu, Jian-Guo Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint. (English) Zbl 1498.80011 J. Stat. Phys. 189, No. 2, Paper No. 22, 57 p. (2022). MSC: 80A32 80A30 44A15 35F21 49L12 60F10 60G55 92C40 81Q20 PDFBibTeX XMLCite \textit{Y. Gao} and \textit{J.-G. Liu}, J. Stat. Phys. 189, No. 2, Paper No. 22, 57 p. (2022; Zbl 1498.80011) Full Text: DOI arXiv
Jüngel, Ansgar; Stefanelli, Ulisse; Trussardi, Lara A minimizing-movements approach to GENERIC systems. (English) Zbl 1503.65313 Math. Eng. (Springfield) 4, No. 1, Paper No. 5, 18 p. (2022). MSC: 65P99 65L05 PDFBibTeX XMLCite \textit{A. Jüngel} et al., Math. Eng. (Springfield) 4, No. 1, Paper No. 5, 18 p. (2022; Zbl 1503.65313) Full Text: DOI arXiv
Forkert, Dominik; Maas, Jan; Portinale, Lorenzo Evolutionary \(\Gamma\)-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. (English) Zbl 1498.35543 SIAM J. Math. Anal. 54, No. 4, 4297-4333 (2022). Reviewer: Dimitris P. Vartziotis (Ioannina) MSC: 35Q84 35A15 65M08 65M12 49Q22 60J65 PDFBibTeX XMLCite \textit{D. Forkert} et al., SIAM J. Math. Anal. 54, No. 4, 4297--4333 (2022; Zbl 1498.35543) Full Text: DOI arXiv
Peletier, Mark A.; Schlottke, Mikola C. Gamma-convergence of a gradient-flow structure to a non-gradient-flow structure. (English) Zbl 1486.35026 Calc. Var. Partial Differ. Equ. 61, No. 3, Paper No. 103, 44 p. (2022). MSC: 35B25 35B27 35K15 35K57 35K67 35R06 37L05 60H10 60F10 70G75 PDFBibTeX XMLCite \textit{M. A. Peletier} and \textit{M. C. Schlottke}, Calc. Var. Partial Differ. Equ. 61, No. 3, Paper No. 103, 44 p. (2022; Zbl 1486.35026) Full Text: DOI arXiv
Peletier, Mark A.; Rossi, Riccarda; Savaré, Giuseppe; Tse, Oliver Jump processes as generalized gradient flows. (English) Zbl 1490.60022 Calc. Var. Partial Differ. Equ. 61, No. 1, Paper No. 33, 85 p. (2022). MSC: 60B20 15B52 35R60 46L54 PDFBibTeX XMLCite \textit{M. A. Peletier} et al., Calc. Var. Partial Differ. Equ. 61, No. 1, Paper No. 33, 85 p. (2022; Zbl 1490.60022) Full Text: DOI arXiv
Mielke, Alexander; Montefusco, Alberto; Peletier, Mark A. Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence. (English) Zbl 1521.37090 Contin. Mech. Thermodyn. 33, No. 3, 611-637 (2021). MSC: 37L05 PDFBibTeX XMLCite \textit{A. Mielke} et al., Contin. Mech. Thermodyn. 33, No. 3, 611--637 (2021; Zbl 1521.37090) Full Text: DOI arXiv
Benamou, Jean-David (ed.); Ehrlacher, Virginie (ed.); Matthes, Daniel (ed.) Applications of optimal transportation in the natural sciences. Abstracts from the workshop held February 21–27, 2021 (online meeting). (English) Zbl 1487.00030 Oberwolfach Rep. 18, No. 1, 507-587 (2021). MSC: 00B05 00B25 49-06 82-06 49Q22 28A33 35Q49 82C70 92Exx PDFBibTeX XMLCite \textit{J.-D. Benamou} (ed.) et al., Oberwolfach Rep. 18, No. 1, 507--587 (2021; Zbl 1487.00030) Full Text: DOI
Heida, Martin; Kantner, Markus; Stephan, Artur Consistency and convergence for a family of finite volume discretizations of the Fokker-Planck operator. (English) Zbl 1485.35356 ESAIM, Math. Model. Numer. Anal. 55, No. 6, 3017-3042 (2021). Reviewer: Abdallah Bradji (Annaba) MSC: 35Q84 49M25 65N08 65N12 65N15 PDFBibTeX XMLCite \textit{M. Heida} et al., ESAIM, Math. Model. Numer. Anal. 55, No. 6, 3017--3042 (2021; Zbl 1485.35356) Full Text: DOI arXiv
Stephan, Artur EDP-convergence for a linear reaction-diffusion system with fast reversible reaction. (English) Zbl 1479.35053 Calc. Var. Partial Differ. Equ. 60, No. 6, Paper No. 226, 35 p. (2021). MSC: 35B25 35K51 35K57 60B05 PDFBibTeX XMLCite \textit{A. Stephan}, Calc. Var. Partial Differ. Equ. 60, No. 6, Paper No. 226, 35 p. (2021; Zbl 1479.35053) Full Text: DOI arXiv
Mielke, Alexander; Peletier, Mark A.; Stephan, Artur EDP-convergence for nonlinear fast-slow reaction systems with detailed balance. (English) Zbl 1475.35183 Nonlinearity 34, No. 8, 5762-5798 (2021). MSC: 35K57 35B25 47J30 92E20 34E13 PDFBibTeX XMLCite \textit{A. Mielke} et al., Nonlinearity 34, No. 8, 5762--5798 (2021; Zbl 1475.35183) Full Text: DOI arXiv
Frenzel, Thomas; Liero, Matthias Effective diffusion in thin structures via generalized gradient systems and EDP-convergence. (English) Zbl 1458.35039 Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 395-425 (2021). MSC: 35B27 35K20 35K10 35K57 35Q84 PDFBibTeX XMLCite \textit{T. Frenzel} and \textit{M. Liero}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 395--425 (2021; Zbl 1458.35039) Full Text: DOI
Maas, Jan; Mielke, Alexander Modeling of chemical reaction systems with detailed balance using gradient structures. (English) Zbl 1462.80011 J. Stat. Phys. 181, No. 6, 2257-2303 (2020). MSC: 80A32 49J45 60J27 82C31 PDFBibTeX XMLCite \textit{J. Maas} and \textit{A. Mielke}, J. Stat. Phys. 181, No. 6, 2257--2303 (2020; Zbl 1462.80011) Full Text: DOI arXiv
Mielke, Alexander; Stephan, Artur Coarse-graining via EDP-convergence for linear fast-slow reaction systems. (English) Zbl 1454.60113 Math. Models Methods Appl. Sci. 30, No. 9, 1765-1807 (2020). MSC: 60J20 47D07 47J30 92E20 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{A. Stephan}, Math. Models Methods Appl. Sci. 30, No. 9, 1765--1807 (2020; Zbl 1454.60113) Full Text: DOI arXiv
Bonaschi, Giovanni A.; Rossi, Riccarda Generation of balanced viscosity solutions to rate-independent systems via variational convergence. (English) Zbl 1435.35011 Ann. Mat. Pura Appl. (4) 199, No. 1, 81-126 (2020). MSC: 35A15 34A60 PDFBibTeX XMLCite \textit{G. A. Bonaschi} and \textit{R. Rossi}, Ann. Mat. Pura Appl. (4) 199, No. 1, 81--126 (2020; Zbl 1435.35011) Full Text: DOI
Kantner, Markus; Mielke, Alexander; Mittnenzweig, Markus; Rotundo, Nella Mathematical modeling of semiconductors: from quantum mechanics to devices. (English) Zbl 1447.35324 Hintermüller, Michael (ed.) et al., Topics in applied analysis and optimisation. Partial differential equations, stochastic and numerical analysis. Selected papers from the Joint CIM-WIAS workshop, TAAO’17, Lisbon, Portugal, December 6–8, 2017. Cham: Springer. CIM Ser. Math. Sci, 269-293 (2019). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q81 82D37 78A35 78A30 82C35 82C10 35Q82 PDFBibTeX XMLCite \textit{M. Kantner} et al., in: Topics in applied analysis and optimisation. Partial differential equations, stochastic and numerical analysis. Selected papers from the Joint CIM-WIAS workshop, TAAO'17, Lisbon, Portugal, December 6--8, 2017. Cham: Springer. 269--293 (2019; Zbl 1447.35324) Full Text: DOI
Dondl, Patrick; Frenzel, Thomas; Mielke, Alexander A gradient system with a wiggly energy and relaxed EDP-convergence. (English) Zbl 1444.35101 ESAIM, Control Optim. Calc. Var. 25, Paper No. 68, 45 p. (2019). MSC: 35K55 35B27 35A15 49S05 49J40 49J45 PDFBibTeX XMLCite \textit{P. Dondl} et al., ESAIM, Control Optim. Calc. Var. 25, Paper No. 68, 45 p. (2019; Zbl 1444.35101) Full Text: DOI arXiv
Bacho, Aras; Emmrich, Etienne; Mielke, Alexander An existence result and evolutionary \(\varGamma \)-convergence for perturbed gradient systems. (English) Zbl 1420.35029 J. Evol. Equ. 19, No. 2, 479-522 (2019). Reviewer: Adrian Muntean (Karlstad) MSC: 35B27 35A15 35K85 49Q20 35K57 35D35 PDFBibTeX XMLCite \textit{A. Bacho} et al., J. Evol. Equ. 19, No. 2, 479--522 (2019; Zbl 1420.35029) Full Text: DOI arXiv
Laschos, Vaios; Mielke, Alexander Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures. (English) Zbl 1422.60009 J. Funct. Anal. 276, No. 11, 3529-3576 (2019). MSC: 60B05 28A33 46E30 PDFBibTeX XMLCite \textit{V. Laschos} and \textit{A. Mielke}, J. Funct. Anal. 276, No. 11, 3529--3576 (2019; Zbl 1422.60009) Full Text: DOI arXiv
Kraaij, Richard; Lazarescu, Alexandre; Maes, Christian; Peletier, Mark Deriving GENERIC from a generalized fluctuation symmetry. (English) Zbl 1390.82045 J. Stat. Phys. 170, No. 3, 492-508 (2018). MSC: 82C31 60F10 60J75 35Q82 PDFBibTeX XMLCite \textit{R. Kraaij} et al., J. Stat. Phys. 170, No. 3, 492--508 (2018; Zbl 1390.82045) Full Text: DOI arXiv
Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander Decay to equilibrium for energy-reaction-diffusion systems. (English) Zbl 1387.35352 SIAM J. Math. Anal. 50, No. 1, 1037-1075 (2018). MSC: 35K57 35B40 35Q79 PDFBibTeX XMLCite \textit{J. Haskovec} et al., SIAM J. Math. Anal. 50, No. 1, 1037--1075 (2018; Zbl 1387.35352) Full Text: DOI arXiv
Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese Cross-diffusion systems with excluded-volume effects and asymptotic gradient flow structures. (English) Zbl 1382.35131 J. Nonlinear Sci. 27, No. 2, 687-719 (2017). MSC: 35K55 35C20 60J70 82C22 35A01 37B25 PDFBibTeX XMLCite \textit{M. Bruna} et al., J. Nonlinear Sci. 27, No. 2, 687--719 (2017; Zbl 1382.35131) Full Text: DOI arXiv
Heinz, Sebastian; Mielke, Alexander Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model. (English) Zbl 1353.82054 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 374, No. 2066, Article ID 20150171, 23 p. (2016). MSC: 82C26 PDFBibTeX XMLCite \textit{S. Heinz} and \textit{A. Mielke}, Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 374, No. 2066, Article ID 20150171, 23 p. (2016; Zbl 1353.82054) Full Text: DOI