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
Mielke, Alexander; Rossi, Riccarda Balanced-viscosity solutions to infinite-dimensional multi-rate systems. (English) Zbl 1514.35107 Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 53, 100 p. (2023). MSC: 35D40 35A15 37B35 47J22 35Q74 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{R. Rossi}, Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 53, 100 p. (2023; Zbl 1514.35107) Full Text: DOI arXiv
Mielke, Alexander On two coupled degenerate parabolic equations motivated by thermodynamics. (English) Zbl 1512.35393 J. Nonlinear Sci. 33, No. 3, Paper No. 42, 55 p. (2023). MSC: 35K65 35K51 35K59 49S05 80M30 PDFBibTeX XMLCite \textit{A. Mielke}, J. Nonlinear Sci. 33, No. 3, Paper No. 42, 55 p. (2023; Zbl 1512.35393) Full Text: DOI arXiv
Mielke, Alexander Relating a rate-independent system and a gradient system for the case of one-homogeneous potentials. (English) Zbl 1509.37108 J. Dyn. Differ. Equations 34, No. 4, 3143-3164 (2022). Reviewer: Panagiotis Koumantos (Athína) MSC: 37L05 47H20 47J35 47J40 PDFBibTeX XMLCite \textit{A. Mielke}, J. Dyn. Differ. Equations 34, No. 4, 3143--3164 (2022; Zbl 1509.37108) Full Text: DOI arXiv
Fischer, Julian; Hopf, Katharina; Kniely, Michael; Mielke, Alexander Global existence analysis of energy-reaction-diffusion systems. (English) Zbl 1483.35262 SIAM J. Math. Anal. 54, No. 1, 220-267 (2022). MSC: 35Q79 35K51 35K57 35D30 35B45 35B65 35A01 80A19 82C35 PDFBibTeX XMLCite \textit{J. Fischer} et al., SIAM J. Math. Anal. 54, No. 1, 220--267 (2022; Zbl 1483.35262) 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
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
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
Mielke, Alexander; Roubíček, Tomáš Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. (English) Zbl 1444.74012 Arch. Ration. Mech. Anal. 238, No. 1, 1-45 (2020). MSC: 74D10 74F05 74H20 35Q74 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{T. Roubíček}, Arch. Ration. Mech. Anal. 238, No. 1, 1--45 (2020; Zbl 1444.74012) Full Text: DOI arXiv
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
Mielke, Alexander; Mittnenzweig, Markus Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities. (English) Zbl 1390.35156 J. Nonlinear Sci. 28, No. 2, 765-806 (2018). MSC: 35K57 35B40 35Q79 92E20 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{M. Mittnenzweig}, J. Nonlinear Sci. 28, No. 2, 765--806 (2018; Zbl 1390.35156) Full Text: DOI
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
Mielke, Alexander (ed.); Peletier, Mark (ed.); Slepcev, Dejan (ed.) Variational methods for evolution. Abstracts from the workshop held November 12–18, 2017. (English) Zbl 1409.00100 Oberwolfach Rep. 14, No. 4, 3185-3261 (2017). MSC: 00B05 00B25 49-06 35-06 70-06 58E30 60F10 82C05 49Jxx PDFBibTeX XMLCite \textit{A. Mielke} (ed.) et al., Oberwolfach Rep. 14, No. 4, 3185--3261 (2017; Zbl 1409.00100) Full Text: DOI
Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel On microscopic origins of generalized gradient structures. (English) Zbl 1515.35127 Discrete Contin. Dyn. Syst., Ser. S 10, No. 1, 1-35 (2017). MSC: 35K55 35Q82 49S05 49J40 49J45 60F10 60J25 PDFBibTeX XMLCite \textit{M. Liero} et al., Discrete Contin. Dyn. Syst., Ser. S 10, No. 1, 1--35 (2017; Zbl 1515.35127) 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
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. (English) Zbl 1347.49078 SIAM J. Math. Anal. 48, No. 4, 2869-2911 (2016). MSC: 49Q20 49K21 58E30 35K57 28A33 46E27 PDFBibTeX XMLCite \textit{M. Liero} et al., SIAM J. Math. Anal. 48, No. 4, 2869--2911 (2016; Zbl 1347.49078) Full Text: DOI arXiv
Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. On uniform decay of the entropy for reaction-diffusion systems. (English) Zbl 1338.35245 J. Dyn. Differ. Equations 27, No. 3-4, 897-928 (2015). MSC: 35K57 35B40 92E20 PDFBibTeX XMLCite \textit{A. Mielke} et al., J. Dyn. Differ. Equations 27, No. 3--4, 897--928 (2015; Zbl 1338.35245) Full Text: DOI
Mielke, Alexander Deriving amplitude equations via evolutionary \(\Gamma\)-convergence. (English) Zbl 1332.35347 Discrete Contin. Dyn. Syst. 35, No. 6, 2679-2700 (2015). MSC: 35Q56 35K55 76E30 47H20 PDFBibTeX XMLCite \textit{A. Mielke}, Discrete Contin. Dyn. Syst. 35, No. 6, 2679--2700 (2015; Zbl 1332.35347) Full Text: DOI
Mielke, Alexander Variational approaches and methods for dissipative material models with multiple scales. (English) Zbl 1365.74087 Conti, Sergio (ed.) et al., Analysis and computation of microstructure in finite plasticity. Cham: Springer (ISBN 978-3-319-18241-4/hbk; 978-3-319-18242-1/ebook). Lecture Notes in Applied and Computational Mechanics 78, 125-155 (2015). MSC: 74G65 74C15 PDFBibTeX XMLCite \textit{A. Mielke}, Lect. Notes Appl. Comput. Mech. 78, 125--155 (2015; Zbl 1365.74087) Full Text: DOI
Mielke, Alexander; Reichelt, Sina; Thomas, Marita Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. (English) Zbl 1304.35052 Netw. Heterog. Media 9, No. 2, 353-382 (2014). MSC: 35B25 35A01 35K57 35K65 35K51 PDFBibTeX XMLCite \textit{A. Mielke} et al., Netw. Heterog. Media 9, No. 2, 353--382 (2014; Zbl 1304.35052) Full Text: DOI
Mielke, Alexander Geodesic convexity of the relative entropy in reversible Markov chains. (English) Zbl 1282.60072 Calc. Var. Partial Differ. Equ. 48, No. 1-2, 1-31 (2013). Reviewer: Piotr Garbaczewski (Opole) MSC: 60J27 53C21 53C23 82C41 82C31 PDFBibTeX XMLCite \textit{A. Mielke}, Calc. Var. Partial Differ. Equ. 48, No. 1--2, 1--31 (2013; Zbl 1282.60072) Full Text: DOI
Glitzky, Annegret; Mielke, Alexander A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. (English) Zbl 1270.35256 Z. Angew. Math. Phys. 64, No. 1, 29-52 (2013). Reviewer: Alexander Mikhajlovich Blokhin (Novosibirsk) MSC: 35K51 35K57 35K58 37L45 78A35 78A57 PDFBibTeX XMLCite \textit{A. Glitzky} and \textit{A. Mielke}, Z. Angew. Math. Phys. 64, No. 1, 29--52 (2013; Zbl 1270.35256) Full Text: DOI
Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan Complete damage in elastic and viscoelastic media and its energetics. (English) Zbl 1227.74058 Comput. Methods Appl. Mech. Eng. 199, No. 21-22, 1242-1253 (2010). MSC: 74R20 74B05 74D05 PDFBibTeX XMLCite \textit{A. Mielke} et al., Comput. Methods Appl. Mech. Eng. 199, No. 21--22, 1242--1253 (2010; Zbl 1227.74058) Full Text: DOI
Thomas, M.; Mielke, A. Damage of nonlinearly elastic materials at small strain – existence and regularity results. (English) Zbl 1191.35159 ZAMM, Z. Angew. Math. Mech. 90, No. 2, 88-112 (2010). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35K85 74C15 74R20 PDFBibTeX XMLCite \textit{M. Thomas} and \textit{A. Mielke}, ZAMM, Z. Angew. Math. Mech. 90, No. 2, 88--112 (2010; Zbl 1191.35159) Full Text: DOI