Edit Profile (opens in new tab) Mielke, Alexander Co-Author Distance Author ID: mielke.alexander Published as: Mielke, Alexander; Mielke, A. Homepage: http://www.wias-berlin.de/people/mielke/ External Links: MGP · ORCID · Wikidata · arXiv · GND · IdRef Documents Indexed: 221 Publications since 1986, including 4 Books and 11 Additional arXiv Preprints 11 Contributions as Editor Biographic References: 1 Publication Co-Authors: 121 Co-Authors with 164 Joint Publications 3,561 Co-Co-Authors all top 5 Co-Authors 66 single-authored 16 Roubíček, Tomáš 14 Savaré, Giuseppe 11 Rossi, Riccarda 10 Peletier, Mark Adriaan 9 Afendikov, Andrei Leonidovich 8 Giannoulis, Johannes 8 Stefanelli, Ulisse 6 Liero, Matthias 5 Knees, Dorothee 5 Petrov, Adrien 5 Schneider, Guido 5 Thomas, Marita 4 Iooss, Gérard 4 Renger, D. R. Michiel 4 Zelik, Sergey V. 3 Hackl, Klaus 3 Herrmann, Michael 3 Holmes, Philip J. 3 Kuczma, Mieczysław S. 3 Mainik, Andreas 3 Mittnenzweig, Markus 3 Naumann, Joachim 3 Paoli, Laetitia A. 3 Reichelt, Sina 3 Schindler, Stefanie 3 Stephan, Artur 3 Zanini, Chiara 2 Bridges, Thomas J. 2 Dreyer, Wolfgang 2 Francfort, Gilles A. 2 Frenzel, Thomas 2 Gallay, Thierry 2 Govindjee, Sanjay 2 Hall, Garrett J. 2 Haskovec, Jan 2 Heinz, Sebastian 2 Hopf, Katharina 2 Kaiser, Hans-Christoph 2 Kirchgässner, Klaus 2 Laschos, Vaios 2 Markowich, Peter Alexander 2 Ortiz, Michael 2 Patz, Carsten 2 Rehberg, Joachim 2 Schmid, Florian 2 Slepčev, Dejan 2 Sparber, Christof 2 Sprenger, Pius 2 Theil, Florian 2 Timofte, Aida M. 2 Wolfrum, Matthias 2 Yanchuk, Sergiĭ Volodymyrovych 1 Abels, Helmut 1 Ambrosio, Luigi 1 Arnrich, Steffen 1 Auricchio, Ferdinando 1 Bacho, Aras 1 Bär, Markus 1 Bartels, Sören 1 Bazaes, Rodrigo 1 Becker, Maximilian 1 Bouchitté, Guy 1 Buffoni, Boris 1 Burylko, Oleksandr 1 Carstensen, Carsten 1 Dal Maso, Gianni 1 Dangelmayr, Gerhard 1 Demay, Yves 1 Disser, Karoline 1 Dondl, Patrick Werner 1 Efendiev, Messoud 1 Emmrich, Etienne 1 Fiedler, Bernold 1 Fischer, Julian 1 Glitzky, Annegret 1 Gürses, Ercan 1 Gussmann, Pascal 1 Heida, Martin 1 Helmig, Rainer 1 Hittmeir, Sabine 1 Huth, Robert 1 Kantner, Markus 1 Kirrmann, Pius 1 Kniely, Michael 1 Kočvara, Michal 1 Koprucki, Thomas 1 Kružík, Martin 1 Kutz, J. Nathan 1 Levitas, Valery I. 1 Lücken, Leonhard 1 Maas, Jan 1 Maltsi, Anieza 1 Martins, João A. C. 1 Miehe, Christian 1 Mittenhuber, Dirk 1 Montefusco, Alberto 1 Mukherjee, Chiranjib 1 Müller, Stefan 1 Netz, Roland R. 1 Niedermayer, Thomas ...and 21 more Co-Authors all top 5 Serials 13 Archive for Rational Mechanics and Analysis 8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Nonlinearity 7 SIAM Journal on Mathematical Analysis 7 Journal of Dynamics and Differential Equations 7 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Journal of Nonlinear Science 6 Calculus of Variations and Partial Differential Equations 6 Oberwolfach Reports 6 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Differential Equations 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Continuum Mechanics and Thermodynamics 4 Discrete and Continuous Dynamical Systems 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 PAMM. Proceedings in Applied Mathematics and Mechanics 3 Mathematical Methods in the Applied Sciences 3 Journal of Elasticity 2 Communications in Mathematical Physics 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Physics 2 Journal of the Mechanics and Physics of Solids 2 Journal of Statistical Physics 2 Rocky Mountain Journal of Mathematics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Mathematische Nachrichten 2 SIAM Journal on Numerical Analysis 2 Physica D 2 SIAM Journal on Applied Mathematics 2 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Convex Analysis 2 Mathematics and Mechanics of Solids 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Evolution Equations 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Advances in Calculus of Variations 1 Applicable Analysis 1 Archives of Mechanics 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Russian Mathematical Surveys 1 Inventiones Mathematicae 1 Journal of Functional Analysis 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Meccanica 1 Memoirs of the American Mathematical Society 1 Zeitschrift für Analysis und ihre Anwendungen 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Asymptotic Analysis 1 European Journal of Mechanics. B. Fluids 1 European Journal of Applied Mathematics 1 Advances in Mathematical Sciences and Applications 1 Potential Analysis 1 Tatra Mountains Mathematical Publications 1 Doklady Mathematics 1 Chaos 1 Journal of Mathematical Fluid Mechanics 1 Nonlinear Analysis. Real World Applications 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Milan Journal of Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 Multiscale Modeling & Simulation 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 GAMM-Mitteilungen 1 Advanced Series in Nonlinear Dynamics 1 Applied Mathematical Sciences 1 Lecture Notes in Mathematics 1 Pitman Research Notes in Mathematics Series 1 Lecture Notes in Applied and Computational Mechanics 1 Networks and Heterogeneous Media 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Journal of Physics. Conference Series all top 5 Fields 132 Partial differential equations (35-XX) 98 Mechanics of deformable solids (74-XX) 53 Calculus of variations and optimal control; optimization (49-XX) 33 Dynamical systems and ergodic theory (37-XX) 33 Fluid mechanics (76-XX) 25 Ordinary differential equations (34-XX) 22 Statistical mechanics, structure of matter (82-XX) 17 Operator theory (47-XX) 12 General and overarching topics; collections (00-XX) 12 Probability theory and stochastic processes (60-XX) 10 Global analysis, analysis on manifolds (58-XX) 10 Mechanics of particles and systems (70-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Numerical analysis (65-XX) 5 Differential geometry (53-XX) 5 Quantum theory (81-XX) 5 Biology and other natural sciences (92-XX) 4 Optics, electromagnetic theory (78-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Geophysics (86-XX) 2 Topological groups, Lie groups (22-XX) 2 Measure and integration (28-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 185 Publications have been cited 4,896 times in 2,140 Documents Cited by ▼ Year ▼ Rate-independent systems. Theory and application. Zbl 1339.35006 Mielke, Alexander; Roubíček, Tomáš 177 2015 Evolution of rate-independent systems. Zbl 1120.47062 Mielke, Alexander 155 2005 Non-convex potentials and microstructures in finite-strain plasticity. Zbl 1008.74016 Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander 139 2002 A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Zbl 1227.35161 Mielke, Alexander 123 2011 On rate-independent hysteresis models. Zbl 1061.35182 Mielke, Alexander; Theil, Florian 123 2004 A variational formulation of rate-independent phase transformations using an extremum principle. Zbl 1012.74054 Mielke, Alexander; Theil, Florian; Levitas, Valery I. 115 2002 Existence results for energetic models for rate-independent systems. Zbl 1161.74387 Mainik, Andreas; Mielke, Alexander 96 2005 \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems. Zbl 1302.49013 Mielke, Alexander; Roubíček, Tomáš; Stefanelli, Ulisse 91 2008 Existence results for a class of rate-independent material models with nonconvex elastic energies. Zbl 1101.74015 Francfort, Gilles; Mielke, Alexander 91 2006 The validity of modulation equations for extended systems with cubic nonlinearities. Zbl 0786.35122 Kirrmann, Pius; Schneider, Guido; Mielke, Alexander 90 1992 Attractors for modulation equations on unbounded domains – existence and comparison. Zbl 0833.35016 Mielke, Alexander; Schneider, Guido 86 1995 Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Zbl 1068.74522 Mielke, A. 82 2003 Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems. Zbl 0747.58001 Mielke, Alexander 82 1991 Reduction of quasilinear equations in cylindrical domains with applications. Zbl 0647.35034 Mielke, Alexander 81 1988 Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Zbl 1412.49089 Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 80 2018 Geodesic convexity of the relative entropy in reversible Markov chains. Zbl 1282.60072 Mielke, Alexander 79 2013 On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion. Zbl 1304.35692 Mielke, A.; Peletier, M. A.; Renger, D. R. M. 78 2014 BV solutions and viscosity approximations of rate-independent systems. Zbl 1250.49041 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 74 2012 Rate-independent damage processes in nonlinear elasticity. Zbl 1094.35068 Mielke, Alexander; Roubíček, Tomáš 70 2006 On the inviscid limit of a model for crack propagation. Zbl 1151.49014 Knees, Dorothee; Mielke, Alexander; Zanini, Chiara 67 2008 On the rate-independent limit of systems with dry friction and small viscosity. Zbl 1109.74040 Efendiev, Messoud A.; Mielke, Alexander 61 2006 A reduction principle for nonautonomous systems in infinite-dimensional spaces. Zbl 0601.35018 Mielke, Alexander 61 1986 Modeling solutions with jumps for rate-independent systems on metric spaces. Zbl 1170.49036 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 54 2009 Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022 Mielke, A.; Holmes, P.; O’Reilly, O. 54 1992 The Ginzburg-Landau equation in its role as a modulation equation. Zbl 1041.37037 Mielke, Alexander 53 2002 Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. Zbl 1347.49078 Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 53 2016 Damage of nonlinearly elastic materials at small strain – existence and regularity results. Zbl 1191.35159 Thomas, M.; Mielke, A. 51 2010 Global existence for rate-independent gradient plasticity at finite strain. Zbl 1173.49013 Mainik, Andreas; Mielke, Alexander 50 2009 Nonsmooth analysis of doubly nonlinear evolution equations. Zbl 1270.35289 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 50 2013 Differential, energetic, and metric formulations for rate-independent processes. Zbl 1251.35003 Mielke, Alexander 47 2011 A proof of the Benjamin-Feir instability. Zbl 0845.76029 Bridges, Thomas J.; Mielke, Alexander 47 1995 The complex Ginzburg-Landau equation on large and unbounded domains: Sharper bounds and attractors. Zbl 0905.35043 Mielke, Alexander 45 1997 Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Zbl 1357.35007 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 45 2016 A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043 Mielke, Alexander; Ortiz, Michael 43 2008 Formulation of thermoelastic dissipative material behavior using GENERIC. Zbl 1272.74137 Mielke, Alexander 43 2011 Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006 Mielke, Alexander; Müller, Stefan 42 2006 Finite elastoplasticity Lie groups and geodesics on \(\text{SL}(d)\). Zbl 1146.74309 Mielke, Alexander 42 2002 Gradient structures and geodesic convexity for reaction-diffusion systems. Zbl 1292.35149 Liero, Matthias; Mielke, Alexander 41 2013 A metric approach to a class of doubly nonlinear evolution equations and applications. Zbl 1183.35164 Rossi, Riccarda; Mielke, Alexander; Savaré, Giuseppe 39 2008 Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi. Zbl 1106.74048 Kružík, Martin; Mielke, Alexander; Roubíček, Tomáš 39 2005 Instability and stability of rolls in the Swift-Hohenberg equation. Zbl 0897.76037 Mielke, Alexander 39 1997 A rate-independent model for inelastic behavior of shape-memory alloys. Zbl 1183.74207 Mielke, Alexander; Roubíček, Tomáš 39 2003 Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. Zbl 1185.35282 Mielke, Alexander; Timofte, Aida M. 36 2007 A spatial dynamics approach to three-dimensional gravity-capillary steady water waves. Zbl 0976.76012 Groves, M. D.; Mielke, A. 36 2001 A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Zbl 1270.35256 Glitzky, Annegret; Mielke, Alexander 34 2013 Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Zbl 1262.35127 Mielke, Alexander 33 2013 A rate-independent approach to the delamination problem. Zbl 1133.74038 Kočvara, Michal; Mielke, Alexander; Roubíček, Tomáš 32 2006 Weighted energy-dissipation functionals for gradient flows. Zbl 1218.35007 Mielke, Alexander; Stefanelli, Ulisse 32 2011 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003 Zelik, Sergey; Mielke, Alexander 32 2009 Existence of minimizers in incremental elasto-plasticity with finite strains. Zbl 1076.74012 Mielke, Alexander 32 2004 Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. Zbl 1270.35055 Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco 32 2012 Existence and uniqueness results for a class of rate-independent hysteresis problems. Zbl 1121.34052 Mielke, Alexander; Rossi, Riccarda 30 2007 A complete-damage problem at small strains. Zbl 1238.74005 Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš 30 2009 A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Zbl 1151.74319 Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse 30 2008 Rate-independent elastoplasticity at finite strains and its numerical approximation. Zbl 1349.35371 Mielke, Alexander; Roubíček, Tomáš 29 2016 Crack growth in polyconvex materials. Zbl 1201.49013 Knees, Dorothee; Zanini, Chiara; Mielke, Alexander 29 2010 Complete damage in elastic and viscoelastic media and its energetics. Zbl 1227.74058 Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan 28 2010 On microscopic origins of generalized gradient structures. Zbl 1515.35127 Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel 28 2017 On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245 Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. 28 2015 Saint-Venant’s problem and semi-inverse solutions in nonlinear elasticity. Zbl 0651.73006 Mielke, Alexander 27 1988 The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities. Zbl 1092.37050 Giannoulis, Johannes; Mielke, Alexander 27 2004 Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity. Zbl 1334.74021 Mielke, Alexander; Stefanelli, Ulisse 27 2013 Spatially complex equilibria of buckled rods. Zbl 0655.73029 Mielke, Alexander; Holmes, Philip 26 1988 Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Zbl 1152.82024 Mielke, Alexander 26 2006 Theory of steady Ginzburg-Landau equation, in hydrodynamic stability problems. Zbl 0675.76060 Iooss, G.; Mielke, A.; Demay, Y. 25 1989 Energy release rate for cracks in finite-strain elasticity. Zbl 1132.74038 Knees, Dorothee; Mielke, Alexander 25 2008 The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis. Zbl 1116.74399 Govindjee, Sanjay; Mielke, Alexander; Hall, Garrett J. 25 2002 Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. Zbl 1248.35105 Bartels, Sören; Mielke, Alexander; Roubíçek, Tomáş 24 2012 Quasiconvexity at the boundary and a simple variational formulation of Agmon’s condition. Zbl 0922.73077 Mielke, Alexander; Sprenger, Pius 24 1998 Normal hyperbolicity of center manifolds and Saint-Venant’s principle. Zbl 0706.73016 Mielke, Alexander 24 1990 Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders. Zbl 0797.76010 Iooss, G.; Mielke, A. 24 1991 Essential manifolds for an elliptic problem in an infinite strip. Zbl 0814.35028 Mielke, Alexander 24 1994 A new identity for the surface-impedance matrix and its application to the determination of surface wave speeds. Zbl 1018.74020 Fu, Y. B.; Mielke, A. 23 2002 An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. Zbl 1376.82046 Mittnenzweig, Markus; Mielke, Alexander 23 2017 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036 Mielke, Alexander; Zelik, Sergey 23 2014 Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. Zbl 1370.80001 Mielke, Alexander; Patterson, Robert I. A.; Peletier, Mark A.; Renger, D. R. Michiel 21 2017 Micro-macro transition in the atomic chain via Whitham’s modulation equation. Zbl 1134.37362 Dreyer, W.; Herrmann, M.; Mielke, A. 20 2006 Deriving new evolution equations for microstructures via relaxation of variational incremental problems. Zbl 1112.74332 Mielke, Alexander 19 2004 Über maximale \(L^ p\)-Regularität für Differentialgleichungen in Banach- und Hilbert-Räumen. (On maximal \(L^ p\)-regularity for differential equations in Banach and Hilbert spaces). Zbl 0597.47029 Mielke, Alexander 19 1987 From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. Zbl 1286.74024 Mielke, Alexander; Truskinovsky, Lev 19 2012 Uniqueness of the surface-wave speed: A proof that it is independent of the Stroh formalism. Zbl 1043.74025 Mielke, Alexander 18 2004 A discrete variational principle for rate-independent evolution. Zbl 1180.35283 Mielke, Alexander; Stefanelli, Ulisse 18 2008 On the energetic stability of solitary water waves. Recent developments in the mathematical theory of water waves (Oberwolfach, 2001). Zbl 1068.76009 Mielke, Alexander 18 2002 Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Zbl 1304.35052 Mielke, Alexander; Reichelt, Sina; Thomas, Marita 18 2014 Necessary and sufficient conditions for polyconvexity of isotropic functions. Zbl 1098.49013 Mielke, Alexander 17 2005 An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness. Zbl 1096.74017 Mielke, Alexander; Timofte, Aida M. 17 2006 Error estimates for space-time discretizations of a rate-independent variational inequality. Zbl 1219.65059 Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse 17 2010 A gradient system with a wiggly energy and relaxed EDP-convergence. Zbl 1444.35101 Dondl, Patrick; Frenzel, Thomas; Mielke, Alexander 17 2019 Variational convergence of gradient flows and rate-independent evolutions in metric spaces. Zbl 1255.49078 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 17 2012 Complete-damage evolution based on energies and stresses. Zbl 1209.74010 Mielke, Alexander 16 2011 Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters. Zbl 0939.35033 Mielke, Alexander 16 1998 Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352 Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander 16 2018 The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis. Zbl 1088.74040 Govindjee, Sanjay; Mielke, Alexander; Hall, Garrett J. 16 2003 A mathematical framework for generalized standard materials in the rate-independent case. Zbl 1298.74006 Mielke, Alexander 15 2006 Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Zbl 1185.35256 Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof 15 2008 From damage to delamination in nonlinearly elastic materials at small strains. Zbl 1253.74088 Mielke, Alexander; Roubíček, Tomáš; Thomas, Marita 15 2012 Global existence results for viscoplasticity at finite strain. Zbl 1387.35574 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 14 2018 Dispersive evolution of pulses in oscillator chains with general interaction potentials. Zbl 1152.34035 Giannoulis, Johannes; Mielke, Alexander 14 2006 Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Zbl 0866.35002 Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander 14 1996 Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. Zbl 1444.74012 Mielke, Alexander; Roubíček, Tomáš 14 2020 Traveling fronts in a reaction-diffusion equation with a memory term. Zbl 07818501 Mielke, Alexander; Reichelt, Sina 1 2024 On two coupled degenerate parabolic equations motivated by thermodynamics. Zbl 1512.35393 Mielke, Alexander 2 2023 Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation. Zbl 1481.35310 Eiter, Thomas; Hopf, Katharina; Mielke, Alexander 4 2022 Global existence analysis of energy-reaction-diffusion systems. Zbl 1483.35262 Fischer, Julian; Hopf, Katharina; Kniely, Michael; Mielke, Alexander 2 2022 Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence. Zbl 1521.37090 Mielke, Alexander; Montefusco, Alberto; Peletier, Mark A. 9 2021 EDP-convergence for nonlinear fast-slow reaction systems with detailed balance. Zbl 1475.35183 Mielke, Alexander; Peletier, Mark A.; Stephan, Artur 6 2021 A rigorous derivation and energetics of a wave equation with fractional damping. Zbl 1483.35165 Mielke, Alexander; Netz, Roland R.; Zendehroud, Sina 1 2021 Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. Zbl 1444.74012 Mielke, Alexander; Roubíček, Tomáš 14 2020 Coarse-graining via EDP-convergence for linear fast-slow reaction systems. Zbl 1454.60113 Mielke, Alexander; Stephan, Artur 13 2020 Modeling of chemical reaction systems with detailed balance using gradient structures. Zbl 1462.80011 Maas, Jan; Mielke, Alexander 13 2020 A gradient system with a wiggly energy and relaxed EDP-convergence. Zbl 1444.35101 Dondl, Patrick; Frenzel, Thomas; Mielke, Alexander 17 2019 Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures. Zbl 1422.60009 Laschos, Vaios; Mielke, Alexander 13 2019 An existence result and evolutionary \(\varGamma \)-convergence for perturbed gradient systems. Zbl 1420.35029 Bacho, Aras; Emmrich, Etienne; Mielke, Alexander 3 2019 Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Zbl 1412.49089 Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 80 2018 Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352 Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander 16 2018 Global existence results for viscoplasticity at finite strain. Zbl 1387.35574 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 14 2018 Coexistence of Hamiltonian-like and dissipative dynamics in rings of coupled phase oscillators with skew-symmetric coupling. Zbl 1401.34040 Burylko, Oleksandr; Mielke, Alexander; Wolfrum, Matthias; Yanchuk, Serhiy 8 2018 Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities. Zbl 1390.35156 Mielke, Alexander; Mittnenzweig, Markus 7 2018 Three examples concerning the interaction of dry friction and oscillations. Zbl 1407.49013 Mielke, Alexander 1 2018 On microscopic origins of generalized gradient structures. Zbl 1515.35127 Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel 28 2017 An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. Zbl 1376.82046 Mittnenzweig, Markus; Mielke, Alexander 23 2017 Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. Zbl 1370.80001 Mielke, Alexander; Patterson, Robert I. A.; Peletier, Mark A.; Renger, D. R. Michiel 21 2017 Averaging of time-periodic dissipation potentials in rate-independent processes. Zbl 1426.34075 Heida, Martin; Mielke, Alexander 2 2017 Uniform asymptotic expansions for the fundamental solution of infinite harmonic chains. Zbl 1386.37074 Mielke, Alexander; Patz, Carsten 1 2017 Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. Zbl 1347.49078 Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 53 2016 Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Zbl 1357.35007 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 45 2016 Rate-independent elastoplasticity at finite strains and its numerical approximation. Zbl 1349.35371 Mielke, Alexander; Roubíček, Tomáš 29 2016 Balanced-viscosity solutions for multi-rate systems. Zbl 1465.70060 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 8 2016 Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model. Zbl 1353.82054 Heinz, Sebastian; Mielke, Alexander 2 2016 Rate-independent systems. Theory and application. Zbl 1339.35006 Mielke, Alexander; Roubíček, Tomáš 177 2015 On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245 Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. 28 2015 Deriving amplitude equations via evolutionary \(\Gamma\)-convergence. Zbl 1332.35347 Mielke, Alexander 7 2015 Global-in-time existence of weak solutions to Kolmogorov’s two-equation model of turbulence. (Sur l’existence globale en temps des solutions faibles pour le modèle de turbulence à deux équations de Kolmogorov.) Zbl 1320.35262 Mielke, Alexander; Naumann, Joachim 7 2015 Global existence for a nonlocal and nonlinear Fokker-Planck equation. Zbl 1325.35227 Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael 6 2015 Spectrum and amplitude equations for scalar delay-differential equations with large delay. Zbl 1312.34100 Yanchuk, Serhiy; Lücken, Leonhard; Wolfrum, Matthias; Mielke, Alexander 6 2015 On thermodynamical couplings of quantum mechanics and macroscopic systems. Zbl 1339.81060 Mielke, A. 5 2015 Variational approaches and methods for dissipative material models with multiple scales. Zbl 1365.74087 Mielke, Alexander 3 2015 On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion. Zbl 1304.35692 Mielke, A.; Peletier, M. A.; Renger, D. R. M. 78 2014 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036 Mielke, Alexander; Zelik, Sergey 23 2014 Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Zbl 1304.35052 Mielke, Alexander; Reichelt, Sina; Thomas, Marita 18 2014 An approach to nonlinear viscoelasticity via metric gradient flows. Zbl 1317.74024 Mielke, Alexander; Ortner, Christoph; Şengül, Yasemin 13 2014 Geodesic convexity of the relative entropy in reversible Markov chains. Zbl 1282.60072 Mielke, Alexander 79 2013 Nonsmooth analysis of doubly nonlinear evolution equations. Zbl 1270.35289 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 50 2013 Gradient structures and geodesic convexity for reaction-diffusion systems. Zbl 1292.35149 Liero, Matthias; Mielke, Alexander 41 2013 A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Zbl 1270.35256 Glitzky, Annegret; Mielke, Alexander 34 2013 Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Zbl 1262.35127 Mielke, Alexander 33 2013 Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity. Zbl 1334.74021 Mielke, Alexander; Stefanelli, Ulisse 27 2013 Dissipative quantum mechanics using GENERIC. Zbl 1315.81061 Mielke, Alexander 9 2013 Homogenization of elastic waves in fluid-saturated porous media using the Biot model. Zbl 1311.35017 Mielke, Alexander; Rohan, Eduard 8 2013 BV solutions and viscosity approximations of rate-independent systems. Zbl 1250.49041 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 74 2012 Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. Zbl 1270.35055 Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco 32 2012 Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. Zbl 1248.35105 Bartels, Sören; Mielke, Alexander; Roubíçek, Tomáş 24 2012 From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. Zbl 1286.74024 Mielke, Alexander; Truskinovsky, Lev 19 2012 Variational convergence of gradient flows and rate-independent evolutions in metric spaces. Zbl 1255.49078 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 17 2012 From damage to delamination in nonlinearly elastic materials at small strains. Zbl 1253.74088 Mielke, Alexander; Roubíček, Tomáš; Thomas, Marita 15 2012 A model for the evolution of laminates in finite-strain elastoplasticity. Zbl 1348.74060 Hackl, K.; Heinz, S.; Mielke, A. 13 2012 Emergence of rate-independent dissipation from viscous systems with wiggly energies. Zbl 1258.74169 Mielke, Alexander 9 2012 A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Zbl 1227.35161 Mielke, Alexander 123 2011 Differential, energetic, and metric formulations for rate-independent processes. Zbl 1251.35003 Mielke, Alexander 47 2011 Formulation of thermoelastic dissipative material behavior using GENERIC. Zbl 1272.74137 Mielke, Alexander 43 2011 Weighted energy-dissipation functionals for gradient flows. Zbl 1218.35007 Mielke, Alexander; Stefanelli, Ulisse 32 2011 Complete-damage evolution based on energies and stresses. Zbl 1209.74010 Mielke, Alexander 16 2011 An evolutionary elastoplastic plate model derived via \(\Gamma\)-convergence. Zbl 1232.35165 Liero, Matthias; Mielke, Alexander 13 2011 On thermodynamically consistent models and gradient structures for thermoplasticity. Zbl 1279.74008 Mielke, Alexander 4 2011 Damage of nonlinearly elastic materials at small strain – existence and regularity results. Zbl 1191.35159 Thomas, M.; Mielke, A. 51 2010 Crack growth in polyconvex materials. Zbl 1201.49013 Knees, Dorothee; Zanini, Chiara; Mielke, Alexander 29 2010 Complete damage in elastic and viscoelastic media and its energetics. Zbl 1227.74058 Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan 28 2010 Error estimates for space-time discretizations of a rate-independent variational inequality. Zbl 1219.65059 Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse 17 2010 Dispersive stability of infinite-dimensional Hamiltonian systems on lattices. Zbl 1200.37071 Mielke, Alexander; Patz, Carsten 9 2010 High-frequency averaging in semi-classical Hartree-type equations. Zbl 1229.35261 Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof 3 2010 Modeling solutions with jumps for rate-independent systems on metric spaces. Zbl 1170.49036 Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 54 2009 Global existence for rate-independent gradient plasticity at finite strain. Zbl 1173.49013 Mainik, Andreas; Mielke, Alexander 50 2009 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003 Zelik, Sergey; Mielke, Alexander 32 2009 A complete-damage problem at small strains. Zbl 1238.74005 Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš 30 2009 On existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys. Zbl 1201.49011 Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien 14 2009 Numerical approaches to rate-independent processes and applications in inelasticity. Zbl 1166.74010 Mielke, Alexander; Roubíček, Tomáš 12 2009 Reverse approximation of energetic solutions to rate-independent processes. Zbl 1163.49030 Mielke, Alexander; Rindler, Filip 8 2009 \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems. Zbl 1302.49013 Mielke, Alexander; Roubíček, Tomáš; Stefanelli, Ulisse 91 2008 On the inviscid limit of a model for crack propagation. Zbl 1151.49014 Knees, Dorothee; Mielke, Alexander; Zanini, Chiara 67 2008 A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043 Mielke, Alexander; Ortiz, Michael 43 2008 A metric approach to a class of doubly nonlinear evolution equations and applications. Zbl 1183.35164 Rossi, Riccarda; Mielke, Alexander; Savaré, Giuseppe 39 2008 A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Zbl 1151.74319 Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse 30 2008 Energy release rate for cracks in finite-strain elasticity. Zbl 1132.74038 Knees, Dorothee; Mielke, Alexander 25 2008 A discrete variational principle for rate-independent evolution. Zbl 1180.35283 Mielke, Alexander; Stefanelli, Ulisse 18 2008 Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Zbl 1185.35256 Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof 15 2008 Weak-convergence methods for Hamiltonian multiscale problems. Zbl 1144.35009 Mielke, Alexander 7 2008 Lagrangian and Hamiltonian two-scale reduction. Zbl 1152.81449 Giannoulis, Johannes; Herrmann, Michael; Mielke, Alexander 6 2008 Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit. Zbl 1147.49004 Mielke, Alexander; Petrov, Adrien; Martins, João A. C. 3 2008 Existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys. Zbl 1393.74034 Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien 1 2008 Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. Zbl 1185.35282 Mielke, Alexander; Timofte, Aida M. 36 2007 Existence and uniqueness results for a class of rate-independent hysteresis problems. Zbl 1121.34052 Mielke, Alexander; Rossi, Riccarda 30 2007 Thermally driven phase transformation in shape-memory alloys. Zbl 1138.49014 Mielke, Alexander; Petrov, Adrien 13 2007 Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in \(\mathbb{R}^n\). Zbl 1125.35012 Mielke, Alexander; Zelik, Sergey V. 4 2007 A model for temperature-induced phase transformations in finite-strain elasticity. Zbl 1128.74035 Mielke, Alexander 3 2007 Existence results for a class of rate-independent material models with nonconvex elastic energies. Zbl 1101.74015 Francfort, Gilles; Mielke, Alexander 91 2006 Rate-independent damage processes in nonlinear elasticity. Zbl 1094.35068 Mielke, Alexander; Roubíček, Tomáš 70 2006 On the rate-independent limit of systems with dry friction and small viscosity. Zbl 1109.74040 Efendiev, Messoud A.; Mielke, Alexander 61 2006 Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006 Mielke, Alexander; Müller, Stefan 42 2006 A rate-independent approach to the delamination problem. Zbl 1133.74038 Kočvara, Michal; Mielke, Alexander; Roubíček, Tomáš 32 2006 Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Zbl 1152.82024 Mielke, Alexander 26 2006 ...and 85 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,128 Authors 106 Mielke, Alexander 56 Stefanelli, Ulisse 53 Schneider, Guido 49 Roubíček, Tomáš 37 Kružík, Martin 36 Rossi, Riccarda 26 Neff, Patrizio 26 Scheel, Arnd 25 Peletier, Mark Adriaan 23 Hackl, Klaus 23 Mosler, Jörn 23 Valls Anglés, Cláudia 20 Savaré, Giuseppe 20 Thomas, Marita 19 Barreira, Luis Manuel 18 Knees, Dorothee 18 Liero, Matthias 17 Conti, Sergio 17 Li, Wuchen 17 Mora, Maria Giovanna 16 Lazzaroni, Giuliano 16 Zelik, Sergey V. 15 Dal Maso, Gianni 15 Francfort, Gilles A. 15 Maas, Jan 14 Akagi, Goro 14 Marigo, Jean-Jacques 14 Miehe, Christian 14 Ortiz, Michael 14 Renger, D. R. Michiel 14 Sandstede, Björn 14 Uecker, Hannes 13 Davoli, Elisa 13 Zanini, Chiara 12 Almi, Stefano 12 Bonetti, Elena 12 Deng, Shengfu 12 Heida, Martin 11 Blömker, Dirk 11 Crismale, Vito 11 Dondl, Patrick Werner 11 Düll, Wolf-Patrick 11 Erbar, Matthias 11 Fellner, Klemens 11 Herrmann, Michael 11 James, Guillaume 11 Krejčí, Pavel 11 Negri, Matteo 11 Solombrino, Francesco 11 Tang, Bao Quoc 11 Toader, Rodica 10 Carstensen, Carsten 10 Dolzmann, Georg 10 Guo, Boling 10 Heinemann, Christian 10 Il’ichev, Andreĭ Teĭmurazovich 10 Iooss, Gérard 10 Junker, Philipp 10 Zimmer, Johannes 9 Benešová, Barbora 9 Bridges, Thomas J. 9 Friedrich, Manuel 9 Ghiba, Ionel-Dumitrel 9 Hur, Vera Mikyoung 9 Kochmann, Dennis M. 9 Kühn, Christian 9 Lloyd, David J. B. 9 Martin, Robert J. 9 Schlichting, André 9 Schmitzer, Bernhard 9 Valdman, Jan 9 Wahlén, Erik 9 Yanchuk, Sergiĭ Volodymyrovych 8 Bartels, Sören 8 Cancès, Clément 8 DeSimone, Antonio 8 Dohnal, Tomáš 8 Duong, Manh Hong 8 Gallay, Thierry 8 Gao, Hongjun 8 Giacomini, Alessandro 8 Jüngel, Ansgar 8 Kovtunenko, Viktor Anatolievich 8 Kraus, Christiane 8 Lerman, Lev 8 Mantič, Vladislav 8 Mariano, Paolo Maria 8 Monsaingeon, Léonard 8 Neukamm, Stefan 8 Pavelka, Michal 8 Pelinovsky, Dmitry Efimovich 8 Petryk, Henryk 8 Riva, Filippo 8 Scala, Riccardo 8 Zumbrun, Kevin R. 7 Alessi, Roberto 7 Babadjian, Jean-François 7 Burger, Martin 7 Champneys, Alan R. 7 Chow, Shui-Nee ...and 2,028 more Authors all top 5 Cited in 300 Serials 107 Archive for Rational Mechanics and Analysis 103 Journal of Differential Equations 74 Physica D 60 Computer Methods in Applied Mechanics and Engineering 56 Continuum Mechanics and Thermodynamics 54 SIAM Journal on Mathematical Analysis 49 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 49 Journal of Nonlinear Science 47 Calculus of Variations and Partial Differential Equations 42 Journal of the Mechanics and Physics of Solids 41 Journal of Dynamics and Differential Equations 41 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 39 ZAMP. Zeitschrift für angewandte Mathematik und Physik 38 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 38 Discrete and Continuous Dynamical Systems. Series S 35 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 34 Journal of Mathematical Analysis and Applications 32 Journal of Elasticity 30 Communications in Mathematical Physics 28 Mathematical Methods in the Applied Sciences 26 Nonlinearity 26 Discrete and Continuous Dynamical Systems 25 Journal of Functional Analysis 24 Journal of Statistical Physics 22 Mathematics and Mechanics of Solids 19 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 18 International Journal for Numerical Methods in Engineering 18 NoDEA. Nonlinear Differential Equations and Applications 18 Journal of Evolution Equations 18 GAMM-Mitteilungen 17 Journal de Mathématiques Pures et Appliquées. Neuvième Série 17 Nonlinear Analysis. Real World Applications 16 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 16 Chaos 16 SIAM Journal on Applied Dynamical Systems 15 Computational Mechanics 14 Applicable Analysis 14 Journal of Mathematical Physics 14 European Journal of Applied Mathematics 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 12 SIAM Journal on Applied Mathematics 12 European Journal of Mechanics. A. Solids 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 International Journal of Engineering Science 11 Journal of Computational Physics 10 Applied Mathematics and Optimization 10 Proceedings of the Royal Society of London. A. 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Matematica e Applicazioni 7 Journal of Mathematical Sciences (New York) 6 Quarterly of Applied Mathematics 6 Studies in Applied Mathematics 6 Applied Mathematical Modelling 6 Journal of Convex Analysis 6 Nonlinear Dynamics 6 Multiscale Modeling & Simulation 6 Kinetic and Related Models 6 Mathematics in Engineering 5 Inventiones Mathematicae 5 Journal of Optimization Theory and Applications 5 Numerische Mathematik 5 Acta Applicandae Mathematicae 5 Applied Mathematics Letters 5 The Annals of Applied Probability 5 Stochastic Processes and their Applications 5 Oberwolfach Reports 4 Computers & Mathematics with Applications 4 International Journal of Solids and Structures 4 Journal of Engineering Mathematics 4 Physica A 4 Mathematics of Computation 4 Advances in Mathematics 4 The Annals of Probability 4 Applied Mathematics and Computation 4 Mathematics and Computers in Simulation 4 Memoirs of the American Mathematical Society 4 Proceedings of the American Mathematical Society 4 Zeitschrift für Analysis und ihre Anwendungen 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Potential Analysis 4 SIAM Journal on Scientific Computing 4 Physics of Fluids ...and 200 more Serials all top 5 Cited in 49 Fields 1,132 Partial differential equations (35-XX) 811 Mechanics of deformable solids (74-XX) 383 Calculus of variations and optimal control; optimization (49-XX) 301 Dynamical systems and ergodic theory (37-XX) 262 Fluid mechanics (76-XX) 179 Ordinary differential equations (34-XX) 162 Numerical analysis (65-XX) 162 Statistical mechanics, structure of matter (82-XX) 157 Probability theory and stochastic processes (60-XX) 117 Operator theory (47-XX) 80 Mechanics of particles and systems (70-XX) 70 Classical thermodynamics, heat transfer (80-XX) 58 Biology and other natural sciences (92-XX) 54 Global analysis, analysis on manifolds (58-XX) 49 Optics, electromagnetic theory (78-XX) 47 Differential geometry (53-XX) 40 Functional analysis (46-XX) 37 Operations research, mathematical programming (90-XX) 33 Quantum theory (81-XX) 31 Measure and integration (28-XX) 22 Difference and functional equations (39-XX) 19 Real functions (26-XX) 16 Systems theory; control (93-XX) 16 Information and communication theory, circuits (94-XX) 13 Integral equations (45-XX) 13 Geophysics (86-XX) 12 Statistics (62-XX) 11 Combinatorics (05-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Computer science (68-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 General and overarching topics; collections (00-XX) 10 General topology (54-XX) 8 Functions of a complex variable (30-XX) 6 Convex and discrete geometry (52-XX) 4 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Geometry (51-XX) 3 Manifolds and cell complexes (57-XX) 2 Integral transforms, operational calculus (44-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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