Edit Profile (opens in new tab) Mielke, Alexander Compute Distance To: Compute 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: 205 Publications since 1986, including 4 Books 11 Contributions as Editor Biographic References: 1 Publication Co-Authors: 119 Co-Authors with 150 Joint Publications 3,188 Co-Co-Authors all top 5 Co-Authors 64 single-authored 14 Roubíček, Tomáš 13 Savaré, Giuseppe 10 Rossi, Riccarda 8 Giannoulis, Johannes 8 Peletier, Mark Adriaan 7 Afendikov, Andrei L. 7 Stefanelli, Ulisse 5 Knees, Dorothee 5 Liero, Matthias 5 Petrov, Adrien 5 Schneider, Guido 5 Thomas, Marita 4 Iooss, Gérard 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 Paoli, Laetitia A. 3 Renger, D. R. Michiel 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 Markowich, Peter Alexander 2 Ortiz, Michael 2 Patz, Carsten 2 Rehberg, Joachim 2 Reichelt, Sina 2 Schmid, Florian 2 Slepčev, Dejan 2 Sparber, Christof 2 Sprenger, Pius 2 Stephan, Artur 2 Theil, Florian 2 Timofte, Aida M. 2 Wolfrum, Matthias 2 Yanchuk, Sergiĭ Volodymyrovych 1 Abels, Helmut 1 Afendikov, Andrej 1 Ambrosio, Luigi 1 Arnrich, Steffen 1 Auricchio, Ferdinando 1 Bacho, Aras 1 Bär, Markus 1 Bartels, Sören 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 Groves, Mark D. 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 Laschos, Vaios 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 Müller, Stefan 1 Naumann, Joachim 1 Netz, Roland R. 1 Niedermayer, Thomas 1 O’Reilly, Oliver Mary 1 Ortner, Christoph ...and 19 more Co-Authors all top 5 Serials 12 Archive for Rational Mechanics and Analysis 8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Nonlinearity 7 SIAM Journal on Mathematical Analysis 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Journal of Dynamics and Differential Equations 6 Journal of Nonlinear Science 6 Calculus of Variations and Partial Differential Equations 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 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 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 3 Continuum Mechanics and Thermodynamics 2 Communications in Mathematical Physics 2 Computer Methods in Applied Mechanics and Engineering 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 Journal of Mathematical Physics 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 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 124 Partial differential equations (35-XX) 96 Mechanics of deformable solids (74-XX) 52 Calculus of variations and optimal control; optimization (49-XX) 32 Dynamical systems and ergodic theory (37-XX) 30 Fluid mechanics (76-XX) 25 Ordinary differential equations (34-XX) 21 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) 7 Classical thermodynamics, heat transfer (80-XX) 6 Numerical analysis (65-XX) 5 Quantum theory (81-XX) 5 Biology and other natural sciences (92-XX) 4 Differential geometry (53-XX) 4 Optics, electromagnetic theory (78-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-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 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 180 Publications have been cited 4,353 times in 1,928 Documents Cited by ▼ Year ▼ Evolution of rate-independent systems. Zbl 1120.47062Mielke, Alexander 142 2005 Rate-independent systems. Theory and application. Zbl 1339.35006Mielke, Alexander; Roubíček, Tomáš 131 2015 Non-convex potentials and microstructures in finite-strain plasticity. Zbl 1008.74016Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander 128 2002 On rate-independent hysteresis models. Zbl 1061.35182Mielke, Alexander; Theil, Florian 115 2004 A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Zbl 1227.35161Mielke, Alexander 108 2011 A variational formulation of rate-independent phase transformations using an extremum principle. Zbl 1012.74054Mielke, Alexander; Theil, Florian; Levitas, Valery I. 108 2002 Existence results for energetic models for rate-independent systems. Zbl 1161.74387Mainik, Andreas; Mielke, Alexander 90 2005 The validity of modulation equations for extended systems with cubic nonlinearities. Zbl 0786.35122Kirrmann, Pius; Schneider, Guido; Mielke, Alexander 84 1992 Attractors for modulation equations on unbounded domains – existence and comparison. Zbl 0833.35016Mielke, Alexander; Schneider, Guido 84 1995 \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems. Zbl 1302.49013Mielke, Alexander; Roubíček, Tomáš; Stefanelli, Ulisse 81 2008 Existence results for a class of rate-independent material models with nonconvex elastic energies. Zbl 1101.74015Francfort, Gilles; Mielke, Alexander 79 2006 Reduction of quasilinear equations in cylindrical domains with applications. Zbl 0647.35034Mielke, Alexander 77 1988 Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems. Zbl 0747.58001Mielke, Alexander 75 1991 Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Zbl 1068.74522Mielke, A. 73 2003 Geodesic convexity of the relative entropy in reversible Markov chains. Zbl 1282.60072Mielke, Alexander 72 2013 BV solutions and viscosity approximations of rate-independent systems. Zbl 1250.49041Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 67 2012 On the inviscid limit of a model for crack propagation. Zbl 1151.49014Knees, Dorothee; Mielke, Alexander; Zanini, Chiara 63 2008 Rate-independent damage processes in nonlinear elasticity. Zbl 1094.35068Mielke, Alexander; Roubíček, Tomáš 59 2006 On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion. Zbl 1304.35692Mielke, A.; Peletier, M. A.; Renger, D. R. M. 59 2014 Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Zbl 1412.49089Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 58 2018 A reduction principle for nonautonomous systems in infinite-dimensional spaces. Zbl 0601.35018Mielke, Alexander 58 1986 On the rate-independent limit of systems with dry friction and small viscosity. Zbl 1109.74040Efendiev, Messoud A.; Mielke, Alexander 56 2006 Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022Mielke, A.; Holmes, P.; O’Reilly, O. 54 1992 The Ginzburg-Landau equation in its role as a modulation equation. Zbl 1041.37037Mielke, Alexander 49 2002 Modeling solutions with jumps for rate-independent systems on metric spaces. Zbl 1170.49036Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 48 2009 Damage of nonlinearly elastic materials at small strain – existence and regularity results. Zbl 1191.35159Thomas, M.; Mielke, A. 45 2010 Global existence for rate-independent gradient plasticity at finite strain. Zbl 1173.49013Mainik, Andreas; Mielke, Alexander 43 2009 The complex Ginzburg-Landau equation on large and unbounded domains: Sharper bounds and attractors. Zbl 0905.35043Mielke, Alexander 43 1997 Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. Zbl 1347.49078Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 42 2016 Differential, energetic, and metric formulations for rate-independent processes. Zbl 1251.35003Mielke, Alexander 42 2011 Nonsmooth analysis of doubly nonlinear evolution equations. Zbl 1270.35289Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 41 2013 Finite elastoplasticity Lie groups and geodesics on \(\text{SL}(d)\). Zbl 1146.74309Mielke, Alexander 41 2002 A proof of the Benjamin-Feir instability. Zbl 0845.76029Bridges, Thomas J.; Mielke, Alexander 39 1995 A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043Mielke, Alexander; Ortiz, Michael 39 2008 Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006Mielke, Alexander; Müller, Stefan 38 2006 Gradient structures and geodesic convexity for reaction-diffusion systems. Zbl 1292.35149Liero, Matthias; Mielke, Alexander 36 2013 Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Zbl 1357.35007Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 36 2016 Formulation of thermoelastic dissipative material behavior using GENERIC. Zbl 1272.74137Mielke, Alexander 36 2011 A spatial dynamics approach to three-dimensional gravity-capillary steady water waves. Zbl 0976.76012Groves, M. D.; Mielke, A. 35 2001 A rate-independent model for inelastic behavior of shape-memory alloys. Zbl 1183.74207Mielke, Alexander; Roubíček, Tomáš 35 2003 Instability and stability of rolls in the Swift-Hohenberg equation. Zbl 0897.76037Mielke, Alexander 35 1997 Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. Zbl 1185.35282Mielke, Alexander; Timofte, Aida M. 35 2007 Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi. Zbl 1106.74048Kružík, Martin; Mielke, Alexander; Roubíček, Tomáš 34 2005 A metric approach to a class of doubly nonlinear evolution equations and applications. Zbl 1183.35164Rossi, Riccarda; Mielke, Alexander; Savaré, Giuseppe 33 2008 Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Zbl 1262.35127Mielke, Alexander 30 2013 A rate-independent approach to the delamination problem. Zbl 1133.74038Kočvara, Michal; Mielke, Alexander; Roubíček, Tomáš 30 2006 Existence of minimizers in incremental elasto-plasticity with finite strains. Zbl 1076.74012Mielke, Alexander 30 2004 Weighted energy-dissipation functionals for gradient flows. Zbl 1218.35007Mielke, Alexander; Stefanelli, Ulisse 29 2011 A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Zbl 1151.74319Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse 29 2008 A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Zbl 1270.35256Glitzky, Annegret; Mielke, Alexander 28 2013 Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. Zbl 1270.35055Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco 28 2012 Existence and uniqueness results for a class of rate-independent hysteresis problems. Zbl 1121.34052Mielke, Alexander; Rossi, Riccarda 27 2007 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 27 2009 A complete-damage problem at small strains. Zbl 1238.74005Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš 27 2009 Saint-Venant’s problem and semi-inverse solutions in nonlinear elasticity. Zbl 0651.73006Mielke, Alexander 27 1988 Complete damage in elastic and viscoelastic media and its energetics. Zbl 1227.74058Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan 27 2010 On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. 26 2015 Crack growth in polyconvex materials. Zbl 1201.49013Knees, Dorothee; Zanini, Chiara; Mielke, Alexander 26 2010 Spatially complex equilibria of buckled rods. Zbl 0655.73029Mielke, Alexander; Holmes, Philip 26 1988 Theory of steady Ginzburg-Landau equation, in hydrodynamic stability problems. Zbl 0675.76060Iooss, G.; Mielke, A.; Demay, Y. 25 1989 The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities. Zbl 1092.37050Giannoulis, Johannes; Mielke, Alexander 25 2004 Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Zbl 1152.82024Mielke, Alexander 24 2006 Normal hyperbolicity of center manifolds and Saint-Venant’s principle. Zbl 0706.73016Mielke, Alexander 24 1990 Energy release rate for cracks in finite-strain elasticity. Zbl 1132.74038Knees, Dorothee; Mielke, Alexander 24 2008 Rate-independent elastoplasticity at finite strains and its numerical approximation. Zbl 1349.35371Mielke, Alexander; Roubíček, Tomáš 23 2016 Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. Zbl 1248.35105Bartels, Sören; Mielke, Alexander; Roubíçek, Tomáş 23 2012 Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders. Zbl 0797.76010Iooss, G.; Mielke, A. 23 1991 The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis. Zbl 1116.74399Govindjee, Sanjay; Mielke, Alexander; Hall, Garrett J. 23 2002 Essential manifolds for an elliptic problem in an infinite strip. Zbl 0814.35028Mielke, Alexander 22 1994 Quasiconvexity at the boundary and a simple variational formulation of Agmon’s condition. Zbl 0922.73077Mielke, Alexander; Sprenger, Pius 22 1998 On microscopic origins of generalized gradient structures. Zbl 06672848Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel 22 2017 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 21 2014 An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. Zbl 1376.82046Mittnenzweig, Markus; Mielke, Alexander 21 2017 A new identity for the surface-impedance matrix and its application to the determination of surface wave speeds. Zbl 1018.74020Fu, Y. B.; Mielke, A. 21 2002 Micro-macro transition in the atomic chain via Whitham’s modulation equation. Zbl 1134.37362Dreyer, W.; Herrmann, M.; Mielke, A. 20 2006 Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity. Zbl 1334.74021Mielke, Alexander; Stefanelli, Ulisse 19 2013 Deriving new evolution equations for microstructures via relaxation of variational incremental problems. Zbl 1112.74332Mielke, Alexander 18 2004 Necessary and sufficient conditions for polyconvexity of isotropic functions. Zbl 1098.49013Mielke, Alexander 17 2005 From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. Zbl 1286.74024Mielke, Alexander; Truskinovsky, Lev 17 2012 A discrete variational principle for rate-independent evolution. Zbl 1180.35283Mielke, Alexander; Stefanelli, Ulisse 17 2008 On the energetic stability of solitary water waves. Recent developments in the mathematical theory of water waves (Oberwolfach, 2001). Zbl 1068.76009Mielke, Alexander 17 2002 Error estimates for space-time discretizations of a rate-independent variational inequality. Zbl 1219.65059Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse 17 2010 Variational convergence of gradient flows and rate-independent evolutions in metric spaces. Zbl 1255.49078Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 16 2012 Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Zbl 1304.35052Mielke, Alexander; Reichelt, Sina; Thomas, Marita 16 2014 Complete-damage evolution based on energies and stresses. Zbl 1209.74010Mielke, Alexander 16 2011 Uniqueness of the surface-wave speed: A proof that it is independent of the Stroh formalism. Zbl 1043.74025Mielke, Alexander 16 2004 The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis. Zbl 1088.74040Govindjee, Sanjay; Mielke, Alexander; Hall, Garrett J. 15 2003 Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. Zbl 1370.80001Mielke, Alexander; Patterson, Robert I. A.; Peletier, Mark A.; Renger, D. R. Michiel 15 2017 An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness. Zbl 1096.74017Mielke, Alexander; Timofte, Aida M. 15 2006 From damage to delamination in nonlinearly elastic materials at small strains. Zbl 1253.74088Mielke, Alexander; Roubíček, Tomáš; Thomas, Marita 15 2012 Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Zbl 1185.35256Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof 15 2008 Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters. Zbl 0939.35033Mielke, Alexander 15 1998 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 0597.47029Mielke, Alexander 14 1987 Dispersive evolution of pulses in oscillator chains with general interaction potentials. Zbl 1152.34035Giannoulis, Johannes; Mielke, Alexander 14 2006 Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander 14 2018 A mathematical framework for generalized standard materials in the rate-independent case. Zbl 1298.74006Mielke, Alexander 14 2006 On existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys. Zbl 1201.49011Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien 14 2009 Thermally driven phase transformation in shape-memory alloys. Zbl 1138.49014Mielke, Alexander; Petrov, Adrien 13 2007 Steady flows of inviscid fluids under localized perturbations. Zbl 0672.76017Mielke, Alexander 12 1986 Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Zbl 0866.35002Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander 12 1996 Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation. Zbl 1481.35310Eiter, Thomas; Hopf, Katharina; Mielke, Alexander 2 2022 Global existence analysis of energy-reaction-diffusion systems. Zbl 1483.35262Fischer, Julian; Hopf, Katharina; Kniely, Michael; Mielke, Alexander 1 2022 EDP-convergence for nonlinear fast-slow reaction systems with detailed balance. Zbl 1475.35183Mielke, Alexander; Peletier, Mark A.; Stephan, Artur 3 2021 Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. Zbl 1444.74012Mielke, Alexander; Roubíček, Tomáš 10 2020 Coarse-graining via EDP-convergence for linear fast-slow reaction systems. Zbl 1454.60113Mielke, Alexander; Stephan, Artur 9 2020 Modeling of chemical reaction systems with detailed balance using gradient structures. Zbl 1462.80011Maas, Jan; Mielke, Alexander 8 2020 A gradient system with a wiggly energy and relaxed EDP-convergence. Zbl 1444.35101Dondl, Patrick; Frenzel, Thomas; Mielke, Alexander 12 2019 Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures. Zbl 1422.60009Laschos, Vaios; Mielke, Alexander 8 2019 An existence result and evolutionary \(\varGamma \)-convergence for perturbed gradient systems. Zbl 1420.35029Bacho, Aras; Emmrich, Etienne; Mielke, Alexander 3 2019 Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Zbl 1412.49089Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 58 2018 Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander 14 2018 Global existence results for viscoplasticity at finite strain. Zbl 1387.35574Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 9 2018 Coexistence of Hamiltonian-like and dissipative dynamics in rings of coupled phase oscillators with skew-symmetric coupling. Zbl 1401.34040Burylko, Oleksandr; Mielke, Alexander; Wolfrum, Matthias; Yanchuk, Serhiy 8 2018 Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities. Zbl 1390.35156Mielke, Alexander; Mittnenzweig, Markus 5 2018 Three examples concerning the interaction of dry friction and oscillations. Zbl 1407.49013Mielke, Alexander 1 2018 On microscopic origins of generalized gradient structures. Zbl 06672848Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel 22 2017 An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. Zbl 1376.82046Mittnenzweig, Markus; Mielke, Alexander 21 2017 Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. Zbl 1370.80001Mielke, Alexander; Patterson, Robert I. A.; Peletier, Mark A.; Renger, D. R. Michiel 15 2017 Averaging of time-periodic dissipation potentials in rate-independent processes. Zbl 1426.34075Heida, Martin; Mielke, Alexander 1 2017 Uniform asymptotic expansions for the fundamental solution of infinite harmonic chains. Zbl 1386.37074Mielke, Alexander; Patz, Carsten 1 2017 Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. Zbl 1347.49078Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe 42 2016 Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Zbl 1357.35007Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 36 2016 Rate-independent elastoplasticity at finite strains and its numerical approximation. Zbl 1349.35371Mielke, Alexander; Roubíček, Tomáš 23 2016 Balanced-viscosity solutions for multi-rate systems. Zbl 1465.70060Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 4 2016 Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model. Zbl 1353.82054Heinz, Sebastian; Mielke, Alexander 2 2016 Rate-independent systems. Theory and application. Zbl 1339.35006Mielke, Alexander; Roubíček, Tomáš 131 2015 On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. 26 2015 Global existence for a nonlocal and nonlinear Fokker-Planck equation. Zbl 1325.35227Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael 6 2015 Deriving amplitude equations via evolutionary \(\Gamma\)-convergence. Zbl 1332.35347Mielke, Alexander 6 2015 Spectrum and amplitude equations for scalar delay-differential equations with large delay. Zbl 1312.34100Yanchuk, Serhiy; Lücken, Leonhard; Wolfrum, Matthias; Mielke, Alexander 6 2015 On thermodynamical couplings of quantum mechanics and macroscopic systems. Zbl 1339.81060Mielke, A. 4 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 1320.35262Mielke, Alexander; Naumann, Joachim 3 2015 Variational approaches and methods for dissipative material models with multiple scales. Zbl 1365.74087Mielke, Alexander 1 2015 On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion. Zbl 1304.35692Mielke, A.; Peletier, M. A.; Renger, D. R. M. 59 2014 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 21 2014 Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Zbl 1304.35052Mielke, Alexander; Reichelt, Sina; Thomas, Marita 16 2014 An approach to nonlinear viscoelasticity via metric gradient flows. Zbl 1317.74024Mielke, Alexander; Ortner, Christoph; Şengül, Yasemin 11 2014 Geodesic convexity of the relative entropy in reversible Markov chains. Zbl 1282.60072Mielke, Alexander 72 2013 Nonsmooth analysis of doubly nonlinear evolution equations. Zbl 1270.35289Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 41 2013 Gradient structures and geodesic convexity for reaction-diffusion systems. Zbl 1292.35149Liero, Matthias; Mielke, Alexander 36 2013 Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Zbl 1262.35127Mielke, Alexander 30 2013 A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Zbl 1270.35256Glitzky, Annegret; Mielke, Alexander 28 2013 Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity. Zbl 1334.74021Mielke, Alexander; Stefanelli, Ulisse 19 2013 Dissipative quantum mechanics using GENERIC. Zbl 1315.81061Mielke, Alexander 8 2013 Homogenization of elastic waves in fluid-saturated porous media using the Biot model. Zbl 1311.35017Mielke, Alexander; Rohan, Eduard 6 2013 BV solutions and viscosity approximations of rate-independent systems. Zbl 1250.49041Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 67 2012 Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction. Zbl 1270.35055Arnrich, Steffen; Mielke, Alexander; Peletier, Mark A.; Savaré, Giuseppe; Veneroni, Marco 28 2012 Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. Zbl 1248.35105Bartels, Sören; Mielke, Alexander; Roubíçek, Tomáş 23 2012 From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. Zbl 1286.74024Mielke, Alexander; Truskinovsky, Lev 17 2012 Variational convergence of gradient flows and rate-independent evolutions in metric spaces. Zbl 1255.49078Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 16 2012 From damage to delamination in nonlinearly elastic materials at small strains. Zbl 1253.74088Mielke, Alexander; Roubíček, Tomáš; Thomas, Marita 15 2012 A model for the evolution of laminates in finite-strain elastoplasticity. Zbl 1348.74060Hackl, K.; Heinz, S.; Mielke, A. 12 2012 Emergence of rate-independent dissipation from viscous systems with wiggly energies. Zbl 1258.74169Mielke, Alexander 6 2012 A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Zbl 1227.35161Mielke, Alexander 108 2011 Differential, energetic, and metric formulations for rate-independent processes. Zbl 1251.35003Mielke, Alexander 42 2011 Formulation of thermoelastic dissipative material behavior using GENERIC. Zbl 1272.74137Mielke, Alexander 36 2011 Weighted energy-dissipation functionals for gradient flows. Zbl 1218.35007Mielke, Alexander; Stefanelli, Ulisse 29 2011 Complete-damage evolution based on energies and stresses. Zbl 1209.74010Mielke, Alexander 16 2011 An evolutionary elastoplastic plate model derived via \(\Gamma\)-convergence. Zbl 1232.35165Liero, Matthias; Mielke, Alexander 12 2011 On thermodynamically consistent models and gradient structures for thermoplasticity. Zbl 1279.74008Mielke, Alexander 4 2011 Damage of nonlinearly elastic materials at small strain – existence and regularity results. Zbl 1191.35159Thomas, M.; Mielke, A. 45 2010 Complete damage in elastic and viscoelastic media and its energetics. Zbl 1227.74058Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan 27 2010 Crack growth in polyconvex materials. Zbl 1201.49013Knees, Dorothee; Zanini, Chiara; Mielke, Alexander 26 2010 Error estimates for space-time discretizations of a rate-independent variational inequality. Zbl 1219.65059Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse 17 2010 Dispersive stability of infinite-dimensional Hamiltonian systems on lattices. Zbl 1200.37071Mielke, Alexander; Patz, Carsten 9 2010 High-frequency averaging in semi-classical Hartree-type equations. Zbl 1229.35261Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof 3 2010 Modeling solutions with jumps for rate-independent systems on metric spaces. Zbl 1170.49036Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe 48 2009 Global existence for rate-independent gradient plasticity at finite strain. Zbl 1173.49013Mainik, Andreas; Mielke, Alexander 43 2009 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 27 2009 A complete-damage problem at small strains. Zbl 1238.74005Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš 27 2009 On existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys. Zbl 1201.49011Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien 14 2009 Numerical approaches to rate-independent processes and applications in inelasticity. Zbl 1166.74010Mielke, Alexander; Roubíček, Tomáš 11 2009 Reverse approximation of energetic solutions to rate-independent processes. Zbl 1163.49030Mielke, Alexander; Rindler, Filip 7 2009 \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems. Zbl 1302.49013Mielke, Alexander; Roubíček, Tomáš; Stefanelli, Ulisse 81 2008 On the inviscid limit of a model for crack propagation. Zbl 1151.49014Knees, Dorothee; Mielke, Alexander; Zanini, Chiara 63 2008 A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043Mielke, Alexander; Ortiz, Michael 39 2008 A metric approach to a class of doubly nonlinear evolution equations and applications. Zbl 1183.35164Rossi, Riccarda; Mielke, Alexander; Savaré, Giuseppe 33 2008 A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Zbl 1151.74319Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse 29 2008 Energy release rate for cracks in finite-strain elasticity. Zbl 1132.74038Knees, Dorothee; Mielke, Alexander 24 2008 A discrete variational principle for rate-independent evolution. Zbl 1180.35283Mielke, Alexander; Stefanelli, Ulisse 17 2008 Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Zbl 1185.35256Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof 15 2008 Weak-convergence methods for Hamiltonian multiscale problems. Zbl 1144.35009Mielke, Alexander 7 2008 Lagrangian and Hamiltonian two-scale reduction. Zbl 1152.81449Giannoulis, Johannes; Herrmann, Michael; Mielke, Alexander 6 2008 Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit. Zbl 1147.49004Mielke, Alexander; Petrov, Adrien; Martins, João A. C. 2 2008 Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. Zbl 1185.35282Mielke, Alexander; Timofte, Aida M. 35 2007 Existence and uniqueness results for a class of rate-independent hysteresis problems. Zbl 1121.34052Mielke, Alexander; Rossi, Riccarda 27 2007 Thermally driven phase transformation in shape-memory alloys. Zbl 1138.49014Mielke, Alexander; Petrov, Adrien 13 2007 Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in \(\mathbb{R}^n\). Zbl 1125.35012Mielke, Alexander; Zelik, Sergey V. 3 2007 A model for temperature-induced phase transformations in finite-strain elasticity. Zbl 1128.74035Mielke, Alexander 2 2007 Existence results for a class of rate-independent material models with nonconvex elastic energies. Zbl 1101.74015Francfort, Gilles; Mielke, Alexander 79 2006 Rate-independent damage processes in nonlinear elasticity. Zbl 1094.35068Mielke, Alexander; Roubíček, Tomáš 59 2006 On the rate-independent limit of systems with dry friction and small viscosity. Zbl 1109.74040Efendiev, Messoud A.; Mielke, Alexander 56 2006 Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006Mielke, Alexander; Müller, Stefan 38 2006 A rate-independent approach to the delamination problem. Zbl 1133.74038Kočvara, Michal; Mielke, Alexander; Roubíček, Tomáš 30 2006 Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Zbl 1152.82024Mielke, Alexander 24 2006 Micro-macro transition in the atomic chain via Whitham’s modulation equation. Zbl 1134.37362Dreyer, W.; Herrmann, M.; Mielke, A. 20 2006 An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness. Zbl 1096.74017Mielke, Alexander; Timofte, Aida M. 15 2006 Dispersive evolution of pulses in oscillator chains with general interaction potentials. Zbl 1152.34035Giannoulis, Johannes; Mielke, Alexander 14 2006 A mathematical framework for generalized standard materials in the rate-independent case. Zbl 1298.74006Mielke, Alexander 14 2006 Continuum descriptions for the dynamics in discrete lattices: derivation and justification. Zbl 1366.82036Giannoulis, Johannes; Herrmann, Michael; Mielke, Alexander 8 2006 ...and 80 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,934 Authors 98 Mielke, Alexander 51 Stefanelli, Ulisse 50 Schneider, Guido 47 Roubíček, Tomáš 34 Rossi, Riccarda 31 Kružík, Martin 26 Neff, Patrizio 24 Scheel, Arnd 22 Peletier, Mark Adriaan 21 Mosler, Jörn 20 Hackl, Klaus 20 Valls Anglés, Cláudia 18 Knees, Dorothee 18 Savaré, Giuseppe 17 Thomas, Marita 16 Barreira, Luis Manuel 16 Conti, Sergio 16 Li, Wuchen 16 Liero, Matthias 16 Mora, Maria Giovanna 15 Dal Maso, Gianni 15 Maas, Jan 14 Francfort, Gilles A. 14 Lazzaroni, Giuliano 14 Miehe, Christian 14 Zelik, Sergey V. 13 Marigo, Jean-Jacques 13 Ortiz, Michael 13 Sandstede, Björn 13 Uecker, Hannes 13 Zanini, Chiara 12 Akagi, Goro 12 Deng, Shengfu 12 Groves, Mark D. 12 Heida, Martin 11 Blömker, Dirk 11 Bonetti, Elena 11 Düll, Wolf-Patrick 11 Erbar, Matthias 11 Negri, Matteo 11 Toader, Rodica 10 Almi, Stefano 10 Bridges, Thomas J. 10 Fellner, Klemens 10 Guo, Boling 10 Heinemann, Christian 10 Herrmann, Michael 10 Iooss, Gérard 10 James, Guillaume 10 Krejčí, Pavel 10 Renger, D. R. Michiel 10 Solombrino, Francesco 9 Carstensen, Carsten 9 Crismale, Vito 9 Davoli, Elisa 9 Ghiba, Ionel-Dumitrel 9 Il’ichev, Andreĭ Teĭmurazovich 9 Martin, Robert J. 9 Schlichting, André 9 Yanchuk, Sergiĭ Volodymyrovych 9 Zimmer, Johannes 8 Bartels, Sören 8 Benešová, Barbora 8 DeSimone, Antonio 8 Dolzmann, Georg 8 Dondl, Patrick Werner 8 Gallay, Thierry 8 Gao, Hongjun 8 Giacomini, Alessandro 8 Hur, Vera Mikyoung 8 Jüngel, Ansgar 8 Junker, Philipp 8 Kochmann, Dennis M. 8 Kovtunenko, Viktor Anatolievich 8 Kraus, Christiane 8 Kühn, Christian 8 Mantič, Vladislav 8 Mariano, Paolo Maria 8 Monsaingeon, Léonard 8 Neukamm, Stefan 8 Pelinovsky, Dmitry Efimovich 8 Tang, Bao Quoc 8 Wahlén, Erik 8 Zumbrun, Kevin R. 7 Alessi, Roberto 7 Champneys, Alan R. 7 Chow, Shui-Nee 7 Dohnal, Tomáš 7 Friedrich, Manuel 7 Grmela, Miroslav 7 Johnson, Mathew A. 7 Khludnev, Aleksandr Mikhaĭlovich 7 Lerman, Lev 7 Lloyd, David J. B. 7 Müller, Stefan 7 Nicholls, David P. 7 Petryk, Henryk 7 Schmitzer, Bernhard 7 Slijepčević, Siniša 7 Svendsen, Bob ...and 1,834 more Authors all top 5 Cited in 271 Serials 104 Archive for Rational Mechanics and Analysis 100 Journal of Differential Equations 71 Physica D 55 Computer Methods in Applied Mechanics and Engineering 51 Continuum Mechanics and Thermodynamics 48 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 45 SIAM Journal on Mathematical Analysis 45 Journal of Nonlinear Science 41 Journal of the Mechanics and Physics of Solids 41 Calculus of Variations and Partial Differential Equations 38 Journal of Dynamics and Differential Equations 37 Discrete and Continuous Dynamical Systems. Series S 36 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 35 ZAMP. Zeitschrift für angewandte Mathematik und Physik 34 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 33 Journal of Mathematical Analysis and Applications 31 Journal of Elasticity 28 Communications in Mathematical Physics 26 Discrete and Continuous Dynamical Systems 26 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 23 Mathematical Methods in the Applied Sciences 22 Journal of Statistical Physics 22 Journal of Functional Analysis 22 Mathematics and Mechanics of Solids 18 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 17 NoDEA. Nonlinear Differential Equations and Applications 16 International Journal for Numerical Methods in Engineering 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 16 Chaos 16 Nonlinear Analysis. Real World Applications 16 GAMM-Mitteilungen 14 Nonlinearity 14 Computational Mechanics 14 European Journal of Applied Mathematics 14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 14 Journal of Evolution Equations 14 SIAM Journal on Applied Dynamical Systems 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Applicable Analysis 12 Journal of Mathematical Physics 11 International Journal of Engineering Science 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 European Journal of Mechanics. A. Solids 10 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 9 Journal of Computational Physics 9 Wave Motion 9 Meccanica 9 Transactions of the American Mathematical Society 9 Communications in Partial Differential Equations 9 SIAM Journal on Applied Mathematics 9 Communications in Nonlinear Science and Numerical Simulation 9 Discrete and Continuous Dynamical Systems. 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Series B 6 Journal of Convex Analysis 6 Nonlinear Dynamics 5 Communications on Pure and Applied Mathematics 5 Inventiones Mathematicae 5 Journal of Optimization Theory and Applications 5 Numerische Mathematik 5 Quarterly of Applied Mathematics 5 Acta Applicandae Mathematicae 5 Applied Mathematics Letters 5 Stochastic Processes and their Applications 5 Multiscale Modeling & Simulation 5 Kinetic and Related Models 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 Memoirs of the American Mathematical Society 4 Proceedings of the American Mathematical Society 4 Studies in Applied Mathematics 4 Zeitschrift für Analysis und ihre Anwendungen 4 The Annals of Applied Probability 4 Applied Mathematical Modelling 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Physics of Fluids 4 Proceedings of the Royal Society of London. 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Mathematical, Physical and Engineering Sciences 4 Journal of Mathematical Fluid Mechanics 4 Journal of the European Mathematical Society (JEMS) 4 Archives of Computational Methods in Engineering 4 Dynamical Systems ...and 171 more Serials all top 5 Cited in 47 Fields 1,023 Partial differential equations (35-XX) 741 Mechanics of deformable solids (74-XX) 341 Calculus of variations and optimal control; optimization (49-XX) 279 Dynamical systems and ergodic theory (37-XX) 237 Fluid mechanics (76-XX) 162 Ordinary differential equations (34-XX) 144 Numerical analysis (65-XX) 144 Statistical mechanics, structure of matter (82-XX) 132 Probability theory and stochastic processes (60-XX) 105 Operator theory (47-XX) 75 Mechanics of particles and systems (70-XX) 61 Classical thermodynamics, heat transfer (80-XX) 49 Biology and other natural sciences (92-XX) 48 Global analysis, analysis on manifolds (58-XX) 45 Optics, electromagnetic theory (78-XX) 42 Differential geometry (53-XX) 33 Quantum theory (81-XX) 30 Functional analysis (46-XX) 30 Operations research, mathematical programming (90-XX) 27 Measure and integration (28-XX) 21 Difference and functional equations (39-XX) 17 Real functions (26-XX) 14 Systems theory; control (93-XX) 11 Geophysics (86-XX) 11 Information and communication theory, circuits (94-XX) 10 Combinatorics (05-XX) 10 Computer science (68-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 General topology (54-XX) 7 General and overarching topics; collections (00-XX) 7 Integral equations (45-XX) 7 Statistics (62-XX) 5 Functions of a complex variable (30-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 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 2 Potential theory (31-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 Special functions (33-XX) 1 Sequences, series, summability (40-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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