Mielke, Alexander; Schindler, Stefanie Existence of similarity profiles for diffusion equations and systems. arXiv:2301.10360 Preprint, arXiv:2301.10360 [math.AP] (2023). MSC: 35C06 35K40 35K57 35K65 80M30 BibTeX Cite \textit{A. Mielke} and \textit{S. Schindler}, ``Existence of similarity profiles for diffusion equations and systems'', Preprint, arXiv:2301.10360 [math.AP] (2023) Full Text: arXiv OA License
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; 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; 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
Liero, Matthias; Mielke, Alexander Gradient structures and geodesic convexity for reaction-diffusion systems. (English) Zbl 1292.35149 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 2005, 20120346, 28 p. (2013). MSC: 35K57 35K51 35K59 PDFBibTeX XMLCite \textit{M. Liero} and \textit{A. Mielke}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 2005, 20120346, 28 p. (2013; Zbl 1292.35149) Full Text: DOI
Mielke, Alexander Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. (English) Zbl 1262.35127 Discrete Contin. Dyn. Syst., Ser. S 6, No. 2, 479-499 (2013). MSC: 35K57 80A17 82B35 74F25 35K51 PDFBibTeX XMLCite \textit{A. Mielke}, Discrete Contin. Dyn. Syst., Ser. S 6, No. 2, 479--499 (2013; Zbl 1262.35127) 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
Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. (English) Zbl 1270.35055 Calc. Var. Partial Differ. Equ. 44, No. 3-4, 419-454 (2012). MSC: 35B27 35K67 35B25 35K20 35K57 60F10 70F40 70G75 37L05 35Q84 PDFBibTeX XMLCite \textit{S. Arnrich} et al., Calc. Var. Partial Differ. Equ. 44, No. 3--4, 419--454 (2012; Zbl 1270.35055) Full Text: DOI arXiv
Mielke, Alexander A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. (English) Zbl 1227.35161 Nonlinearity 24, No. 4, 1329-1346 (2011). Reviewer: Gisèle M. Mophou (Pointe-à-Pitre) MSC: 35K51 35K57 35K58 PDFBibTeX XMLCite \textit{A. Mielke}, Nonlinearity 24, No. 4, 1329--1346 (2011; Zbl 1227.35161) Full Text: DOI
Mielke, Alexander; Zelik, Sergey V. Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in \(\mathbb{R}^n\). (English) Zbl 1125.35012 J. Dyn. Differ. Equations 19, No. 2, 333-389 (2007). Reviewer: Christian Pötzsche (München) MSC: 35B40 35K57 37L30 37B40 37D45 37L45 35B41 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{S. V. Zelik}, J. Dyn. Differ. Equations 19, No. 2, 333--389 (2007; Zbl 1125.35012) Full Text: DOI
Afendikov, Andrei; Mielke, Alexander Multi-pulse solutions in problems with reflection symmetry in cylindrical domains. (English) Zbl 0971.35039 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 769-771 (2000). MSC: 35K57 37L15 35B10 37L20 PDFBibTeX XMLCite \textit{A. Afendikov} and \textit{A. Mielke}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 769--771 (2000; Zbl 0971.35039)
Mielke, Alexander Exponentially weighted \(L^{\infty}\)-estimates and attractors for parabolic systems on unbounded domains. (English) Zbl 0966.37040 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 641-646 (2000). MSC: 37L30 35K57 PDFBibTeX XMLCite \textit{A. Mielke}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 641--646 (2000; Zbl 0966.37040)