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; 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; Netz, Roland R.; Zendehroud, Sina A rigorous derivation and energetics of a wave equation with fractional damping. (English) Zbl 1483.35165 J. Evol. Equ. 21, No. 3, 3079-3102 (2021). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 35Q74 74F10 74J15 74K15 35B40 35A01 26A33 35R11 PDFBibTeX XMLCite \textit{A. Mielke} et al., J. Evol. Equ. 21, No. 3, 3079--3102 (2021; Zbl 1483.35165) 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
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
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe Global existence results for viscoplasticity at finite strain. (English) Zbl 1387.35574 Arch. Ration. Mech. Anal. 227, No. 1, 423-475 (2018). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q74 74D10 35A01 PDFBibTeX XMLCite \textit{A. Mielke} et al., Arch. Ration. Mech. Anal. 227, No. 1, 423--475 (2018; Zbl 1387.35574) Full Text: DOI arXiv
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
Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael Global existence for a nonlocal and nonlinear Fokker-Planck equation. (English) Zbl 1325.35227 Z. Angew. Math. Phys. 66, No. 2, 293-315 (2015). MSC: 35Q84 35A01 35C20 35B40 PDFBibTeX XMLCite \textit{W. Dreyer} et al., Z. Angew. Math. Phys. 66, No. 2, 293--315 (2015; Zbl 1325.35227) Full Text: DOI
Mielke, Alexander; Stefanelli, Ulisse A discrete variational principle for rate-independent evolution. (English) Zbl 1180.35283 Adv. Calc. Var. 1, No. 4, 399-431 (2008). Reviewer: M. Marin (Brasov) MSC: 35K55 35R35 49J40 49K20 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{U. Stefanelli}, Adv. Calc. Var. 1, No. 4, 399--431 (2008; Zbl 1180.35283) Full Text: DOI
Mielke, Alexander; Ortiz, Michael A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. (English) Zbl 1357.49043 ESAIM, Control Optim. Calc. Var. 14, No. 3, 494-516 (2008). MSC: 49J40 49M20 49S05 74N10 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{M. Ortiz}, ESAIM, Control Optim. Calc. Var. 14, No. 3, 494--516 (2008; Zbl 1357.49043) Full Text: DOI EuDML
Mielke, Alexander A model for temperature-induced phase transformations in finite-strain elasticity. (English) Zbl 1128.74035 IMA J. Appl. Math. 72, No. 5, 644-658 (2007). MSC: 74N30 74B20 74F05 74G65 PDFBibTeX XMLCite \textit{A. Mielke}, IMA J. Appl. Math. 72, No. 5, 644--658 (2007; Zbl 1128.74035) Full Text: DOI
Mielke, Alexander; Timofte, Aida M. An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness. (English) Zbl 1096.74017 Math. Methods Appl. Sci. 29, No. 12, 1393-1410 (2006). MSC: 74F15 74G65 74H20 74H25 82D45 PDFBibTeX XMLCite \textit{A. Mielke} and \textit{A. M. Timofte}, Math. Methods Appl. Sci. 29, No. 12, 1393--1410 (2006; Zbl 1096.74017) Full Text: DOI
Kružík, Martin; Mielke, Alexander; Roubíček, Tomáš Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi. (English) Zbl 1106.74048 Meccanica 40, No. 5-6, 389-418 (2005). MSC: 74N05 74G65 PDFBibTeX XMLCite \textit{M. Kružík} et al., Meccanica 40, No. 5--6, 389--418 (2005; Zbl 1106.74048) Full Text: DOI
Hackl, Klaus; Mielke, Alexander; Mittenhuber, Dirk Dissipation distances in multiplicative elastoplasticity. (English) Zbl 1095.74005 Wendland, Wolfgang (ed.) et al., Analysis and simulation of multifield problems. Selected papers of the international conference on multifield problems, Stuttgart, Germany, April 8–10, 2002. Berlin: Springer (ISBN 3-540-00696-6/hbk). Lect. Notes Appl. Comput. Mech. 12, 87-100 (2003). MSC: 74C15 PDFBibTeX XMLCite \textit{K. Hackl} et al., Lect. Notes Appl. Comput. Mech. 12, 87--100 (2003; Zbl 1095.74005)
Mielke, A. Evolution of rate-independent inelasticity with microstructure using relaxation and Young measures. (English) Zbl 1040.74011 Miehe, Christian (ed.), IUTAM symposium on computational mechanics of solid materials at large strains. Proceedings of the IUTAM symposium, Stuttgart, Germany, August 20–24, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1170-9/hbk). Solid Mech. Appl. 108, 33-44 (2003). MSC: 74C15 74A60 74G65 PDFBibTeX XMLCite \textit{A. Mielke}, Solid Mech. Appl. 108, 33--44 (2003; Zbl 1040.74011)
Mielke, A. Energetic formulation of multiplicative elasto-plasticity using dissipation distances. (English) Zbl 1068.74522 Contin. Mech. Thermodyn. 15, No. 4, 351-382 (2003). MSC: 74C15 74G65 PDFBibTeX XMLCite \textit{A. Mielke}, Contin. Mech. Thermodyn. 15, No. 4, 351--382 (2003; Zbl 1068.74522) Full Text: DOI
Mielke, Alexander Analysis of energetic models for rate-independent materials. (English) Zbl 1018.74007 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press. 817-828 (2002). Reviewer: N.Cristescu (Gainesville) MSC: 74C15 74G65 PDFBibTeX XMLCite \textit{A. Mielke}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 817--828 (2002; Zbl 1018.74007) Full Text: arXiv
Mielke, Alexander; Theil, Florian; Levitas, Valery I. A variational formulation of rate-independent phase transformations using an extremum principle. (English) Zbl 1012.74054 Arch. Ration. Mech. Anal. 162, No. 2, 137-177 (2002). MSC: 74N30 74N15 82B26 PDFBibTeX XMLCite \textit{A. Mielke} et al., Arch. Ration. Mech. Anal. 162, No. 2, 137--177 (2002; Zbl 1012.74054) Full Text: DOI
Kuczma, M. S.; Mielke, A.; Stein, Erwin Modelling of hysteresis in two-phase systems. (English) Zbl 0990.74048 Arch. Mech. 51, No. 6, 693-715 (1999). MSC: 74N30 74A15 PDFBibTeX XMLCite \textit{M. S. Kuczma} et al., Arch. Mech. 51, No. 6, 693--715 (1999; Zbl 0990.74048)