## Mielke, Alexander

Compute Distance To:
 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: 202 Publications since 1986, including 4 Books 11 Contributions as Editor Biographic References: 1 Publication Co-Authors: 119 Co-Authors with 149 Joint Publications 3,051 Co-Co-Authors
all top 5

### Co-Authors

 62 single-authored 14 Roubíček, Tomáš 13 Savaré, Giuseppe 9 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

 11 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 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 5 Journal of Dynamics and Differential Equations 5 Journal of Nonlinear Science 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

 122 Partial differential equations (35-XX) 96 Mechanics of deformable solids (74-XX) 51 Calculus of variations and optimal control; optimization (49-XX) 30 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) 15 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) 6 Numerical analysis (65-XX) 6 Classical thermodynamics, heat transfer (80-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)

### Citations contained in zbMATH Open

179 Publications have been cited 4,008 times in 1,790 Documents Cited by Year
Evolution of rate-independent systems. Zbl 1120.47062
Mielke, Alexander
2005
Non-convex potentials and microstructures in finite-strain plasticity. Zbl 1008.74016
Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander
2002
On rate-independent hysteresis models. Zbl 1061.35182
Mielke, Alexander; Theil, Florian
2004
Rate-independent systems. Theory and application. Zbl 1339.35006
Mielke, Alexander; Roubíček, Tomáš
2015
A variational formulation of rate-independent phase transformations using an extremum principle. Zbl 1012.74054
Mielke, Alexander; Theil, Florian; Levitas, Valery I.
2002
A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Zbl 1227.35161
Mielke, Alexander
2011
Existence results for energetic models for rate-independent systems. Zbl 1161.74387
Mainik, Andreas; Mielke, Alexander
2005
The validity of modulation equations for extended systems with cubic nonlinearities. Zbl 0786.35122
Kirrmann, Pius; Schneider, Guido; Mielke, Alexander
1992
Attractors for modulation equations on unbounded domains – existence and comparison. Zbl 0833.35016
Mielke, Alexander; Schneider, Guido
1995
$$\Gamma$$-limits and relaxations for rate-independent evolutionary problems. Zbl 1302.49013
Mielke, Alexander; Roubíček, Tomáš; Stefanelli, Ulisse
2008
Existence results for a class of rate-independent material models with nonconvex elastic energies. Zbl 1101.74015
Francfort, Gilles; Mielke, Alexander
2006
Reduction of quasilinear equations in cylindrical domains with applications. Zbl 0647.35034
Mielke, Alexander
1988
Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Zbl 1068.74522
Mielke, A.
2003
Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems. Zbl 0747.58001
Mielke, Alexander
1991
Geodesic convexity of the relative entropy in reversible Markov chains. Zbl 1282.60072
Mielke, Alexander
2013
BV solutions and viscosity approximations of rate-independent systems. Zbl 1250.49041
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2012
On the inviscid limit of a model for crack propagation. Zbl 1151.49014
Knees, Dorothee; Mielke, Alexander; Zanini, Chiara
2008
A reduction principle for nonautonomous systems in infinite-dimensional spaces. Zbl 0601.35018
Mielke, Alexander
1986
Rate-independent damage processes in nonlinear elasticity. Zbl 1094.35068
Mielke, Alexander; Roubíček, Tomáš
2006
Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022
Mielke, A.; Holmes, P.; O’Reilly, O.
1992
On the rate-independent limit of systems with dry friction and small viscosity. Zbl 1109.74040
Efendiev, Messoud A.; Mielke, Alexander
2006
Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Zbl 1412.49089
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
2018
The Ginzburg-Landau equation in its role as a modulation equation. Zbl 1041.37037
Mielke, Alexander
2002
Damage of nonlinearly elastic materials at small strain – existence and regularity results. Zbl 1191.35159
Thomas, M.; Mielke, A.
2010
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.
2014
The complex Ginzburg-Landau equation on large and unbounded domains: Sharper bounds and attractors. Zbl 0905.35043
Mielke, Alexander
1997
Differential, energetic, and metric formulations for rate-independent processes. Zbl 1251.35003
Mielke, Alexander
2011
Modeling solutions with jumps for rate-independent systems on metric spaces. Zbl 1170.49036
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2009
Finite elastoplasticity Lie groups and geodesics on $$\text{SL}(d)$$. Zbl 1146.74309
Mielke, Alexander
2002
Global existence for rate-independent gradient plasticity at finite strain. Zbl 1173.49013
Mainik, Andreas; Mielke, Alexander
2009
Nonsmooth analysis of doubly nonlinear evolution equations. Zbl 1270.35289
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2013
A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043
Mielke, Alexander; Ortiz, Michael
2008
Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006
Mielke, Alexander; Müller, Stefan
2006
Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. Zbl 1347.49078
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
2016
A spatial dynamics approach to three-dimensional gravity-capillary steady water waves. Zbl 0976.76012
Groves, M. D.; Mielke, A.
2001
Gradient structures and geodesic convexity for reaction-diffusion systems. Zbl 1292.35149
Liero, Matthias; Mielke, Alexander
2013
A rate-independent model for inelastic behavior of shape-memory alloys. Zbl 1183.74207
Mielke, Alexander; Roubíček, Tomáš
2003
A proof of the Benjamin-Feir instability. Zbl 0845.76029
Bridges, Thomas J.; Mielke, Alexander
1995
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
2005
Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. Zbl 1185.35282
Mielke, Alexander; Timofte, Aida M.
2007
Instability and stability of rolls in the Swift-Hohenberg equation. Zbl 0897.76037
Mielke, Alexander
1997
Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Zbl 1357.35007
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2016
Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Zbl 1262.35127
Mielke, Alexander
2013
Formulation of thermoelastic dissipative material behavior using GENERIC. Zbl 1272.74137
Mielke, Alexander
2011
Existence of minimizers in incremental elasto-plasticity with finite strains. Zbl 1076.74012
Mielke, Alexander
2004
A rate-independent approach to the delamination problem. Zbl 1133.74038
Kočvara, Michal; Mielke, Alexander; Roubíček, Tomáš
2006
A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Zbl 1151.74319
Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse
2008
Complete damage in elastic and viscoelastic media and its energetics. Zbl 1227.74058
Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan
2010
Saint-Venant’s problem and semi-inverse solutions in nonlinear elasticity. Zbl 0651.73006
Mielke, Alexander
1988
A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Zbl 1270.35256
Glitzky, Annegret; Mielke, Alexander
2013
Existence and uniqueness results for a class of rate-independent hysteresis problems. Zbl 1121.34052
Mielke, Alexander; Rossi, Riccarda
2007
A metric approach to a class of doubly nonlinear evolution equations and applications. Zbl 1183.35164
Rossi, Riccarda; Mielke, Alexander; Savaré, Giuseppe
2008
Weighted energy-dissipation functionals for gradient flows. Zbl 1218.35007
Mielke, Alexander; Stefanelli, Ulisse
2011
On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245
Mielke, Alexander; Haskovec, Jan; Markowich, Peter A.
2015
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
2012
Spatially complex equilibria of buckled rods. Zbl 0655.73029
Mielke, Alexander; Holmes, Philip
1988
A complete-damage problem at small strains. Zbl 1238.74005
Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš
2009
Theory of steady Ginzburg-Landau equation, in hydrodynamic stability problems. Zbl 0675.76060
Iooss, G.; Mielke, A.; Demay, Y.
1989
The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities. Zbl 1092.37050
Giannoulis, Johannes; Mielke, Alexander
2004
Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. Zbl 1248.35105
Bartels, Sören; Mielke, Alexander; Roubíçek, Tomáş
2012
Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Zbl 1152.82024
Mielke, Alexander
2006
Normal hyperbolicity of center manifolds and Saint-Venant’s principle. Zbl 0706.73016
Mielke, Alexander
1990
Crack growth in polyconvex materials. Zbl 1201.49013
Knees, Dorothee; Zanini, Chiara; Mielke, Alexander
2010
Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003
Zelik, Sergey; Mielke, Alexander
2009
Energy release rate for cracks in finite-strain elasticity. Zbl 1132.74038
Knees, Dorothee; Mielke, Alexander
2008
Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders. Zbl 0797.76010
Iooss, G.; Mielke, A.
1991
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.
2002
Quasiconvexity at the boundary and a simple variational formulation of Agmon’s condition. Zbl 0922.73077
Mielke, Alexander; Sprenger, Pius
1998
Rate-independent elastoplasticity at finite strains and its numerical approximation. Zbl 1349.35371
Mielke, Alexander; Roubíček, Tomáš
2016
Essential manifolds for an elliptic problem in an infinite strip. Zbl 0814.35028
Mielke, Alexander
1994
Micro-macro transition in the atomic chain via Whitham’s modulation equation. Zbl 1134.37362
Dreyer, W.; Herrmann, M.; Mielke, A.
2006
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.
2002
On microscopic origins of generalized gradient structures. Zbl 06672848
Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel
2017
Deriving new evolution equations for microstructures via relaxation of variational incremental problems. Zbl 1112.74332
Mielke, Alexander
2004
On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036
Mielke, Alexander; Zelik, Sergey
2014
An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. Zbl 1376.82046
Mittnenzweig, Markus; Mielke, Alexander
2017
From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. Zbl 1286.74024
Mielke, Alexander; Truskinovsky, Lev
2012
Linearized plasticity is the evolutionary $$\Gamma$$-limit of finite plasticity. Zbl 1334.74021
Mielke, Alexander; Stefanelli, Ulisse
2013
On the energetic stability of solitary water waves. Recent developments in the mathematical theory of water waves (Oberwolfach, 2001). Zbl 1068.76009
Mielke, Alexander
2002
A discrete variational principle for rate-independent evolution. Zbl 1180.35283
Mielke, Alexander; Stefanelli, Ulisse
2008
Necessary and sufficient conditions for polyconvexity of isotropic functions. Zbl 1098.49013
Mielke, Alexander
2005
An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness. Zbl 1096.74017
Mielke, Alexander; Timofte, Aida M.
2006
Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters. Zbl 0939.35033
Mielke, Alexander
1998
From damage to delamination in nonlinearly elastic materials at small strains. Zbl 1253.74088
Mielke, Alexander; Roubíček, Tomáš; Thomas, Marita
2012
Uniqueness of the surface-wave speed: A proof that it is independent of the Stroh formalism. Zbl 1043.74025
Mielke, Alexander
2004
Error estimates for space-time discretizations of a rate-independent variational inequality. Zbl 1219.65059
Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse
2010
Dispersive evolution of pulses in oscillator chains with general interaction potentials. Zbl 1152.34035
Giannoulis, Johannes; Mielke, Alexander
2006
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
2009
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.
2003
Complete-damage evolution based on energies and stresses. Zbl 1209.74010
Mielke, Alexander
2011
A mathematical framework for generalized standard materials in the rate-independent case. Zbl 1298.74006
Mielke, Alexander
2006
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
1987
Variational convergence of gradient flows and rate-independent evolutions in metric spaces. Zbl 1255.49078
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2012
Thermally driven phase transformation in shape-memory alloys. Zbl 1138.49014
2007
Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Zbl 1185.35256
Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof
2008
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
2017
Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Zbl 1304.35052
Mielke, Alexander; Reichelt, Sina; Thomas, Marita
2014
An evolutionary elastoplastic plate model derived via $$\Gamma$$-convergence. Zbl 1232.35165
Liero, Matthias; Mielke, Alexander
2011
On Saint-Venant’s problem for an elastic strip. Zbl 0657.73003
Mielke, Alexander
1988
Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352
Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander
2018
Global existence analysis of energy-reaction-diffusion systems. Zbl 1483.35262
Fischer, Julian; Hopf, Katharina; Kniely, Michael; Mielke, Alexander
2022
Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation. Zbl 1481.35310
Eiter, Thomas; Hopf, Katharina; Mielke, Alexander
2022
EDP-convergence for nonlinear fast-slow reaction systems with detailed balance. Zbl 1475.35183
Mielke, Alexander; Peletier, Mark A.; Stephan, Artur
2021
Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. Zbl 1444.74012
Mielke, Alexander; Roubíček, Tomáš
2020
Coarse-graining via EDP-convergence for linear fast-slow reaction systems. Zbl 1454.60113
Mielke, Alexander; Stephan, Artur
2020
Modeling of chemical reaction systems with detailed balance using gradient structures. Zbl 1462.80011
Maas, Jan; Mielke, Alexander
2020
A gradient system with a wiggly energy and relaxed EDP-convergence. Zbl 1444.35101
Dondl, Patrick; Frenzel, Thomas; Mielke, Alexander
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
2019
An existence result and evolutionary $$\varGamma$$-convergence for perturbed gradient systems. Zbl 1420.35029
Bacho, Aras; Emmrich, Etienne; Mielke, Alexander
2019
Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Zbl 1412.49089
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
2018
Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352
Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander
2018
Global existence results for viscoplasticity at finite strain. Zbl 1387.35574
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
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
2018
Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities. Zbl 1390.35156
Mielke, Alexander; Mittnenzweig, Markus
2018
Three examples concerning the interaction of dry friction and oscillations. Zbl 1407.49013
Mielke, Alexander
2018
On microscopic origins of generalized gradient structures. Zbl 06672848
Liero, Matthias; Mielke, Alexander; Peletier, Mark; Renger, D. R. Michiel
2017
An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models. Zbl 1376.82046
Mittnenzweig, Markus; Mielke, Alexander
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
2017
Averaging of time-periodic dissipation potentials in rate-independent processes. Zbl 1426.34075
Heida, Martin; Mielke, Alexander
2017
Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. Zbl 1347.49078
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
2016
Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Zbl 1357.35007
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2016
Rate-independent elastoplasticity at finite strains and its numerical approximation. Zbl 1349.35371
Mielke, Alexander; Roubíček, Tomáš
2016
Balanced-viscosity solutions for multi-rate systems. Zbl 1465.70060
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2016
Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model. Zbl 1353.82054
Heinz, Sebastian; Mielke, Alexander
2016
Rate-independent systems. Theory and application. Zbl 1339.35006
Mielke, Alexander; Roubíček, Tomáš
2015
On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245
Mielke, Alexander; Haskovec, Jan; Markowich, Peter A.
2015
Global existence for a nonlocal and nonlinear Fokker-Planck equation. Zbl 1325.35227
Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael
2015
Deriving amplitude equations via evolutionary $$\Gamma$$-convergence. Zbl 1332.35347
Mielke, Alexander
2015
Spectrum and amplitude equations for scalar delay-differential equations with large delay. Zbl 1312.34100
Yanchuk, Serhiy; Lücken, Leonhard; Wolfrum, Matthias; Mielke, Alexander
2015
On thermodynamical couplings of quantum mechanics and macroscopic systems. Zbl 1339.81060
Mielke, A.
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
2015
Variational approaches and methods for dissipative material models with multiple scales. Zbl 1365.74087
Mielke, Alexander
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.
2014
On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036
Mielke, Alexander; Zelik, Sergey
2014
Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Zbl 1304.35052
Mielke, Alexander; Reichelt, Sina; Thomas, Marita
2014
An approach to nonlinear viscoelasticity via metric gradient flows. Zbl 1317.74024
Mielke, Alexander; Ortner, Christoph; Şengül, Yasemin
2014
Geodesic convexity of the relative entropy in reversible Markov chains. Zbl 1282.60072
Mielke, Alexander
2013
Nonsmooth analysis of doubly nonlinear evolution equations. Zbl 1270.35289
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2013
Gradient structures and geodesic convexity for reaction-diffusion systems. Zbl 1292.35149
Liero, Matthias; Mielke, Alexander
2013
Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Zbl 1262.35127
Mielke, Alexander
2013
A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Zbl 1270.35256
Glitzky, Annegret; Mielke, Alexander
2013
Linearized plasticity is the evolutionary $$\Gamma$$-limit of finite plasticity. Zbl 1334.74021
Mielke, Alexander; Stefanelli, Ulisse
2013
Dissipative quantum mechanics using GENERIC. Zbl 1315.81061
Mielke, Alexander
2013
Homogenization of elastic waves in fluid-saturated porous media using the Biot model. Zbl 1311.35017
Mielke, Alexander; Rohan, Eduard
2013
BV solutions and viscosity approximations of rate-independent systems. Zbl 1250.49041
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
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
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
2012
From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. Zbl 1286.74024
Mielke, Alexander; Truskinovsky, Lev
2012
From damage to delamination in nonlinearly elastic materials at small strains. Zbl 1253.74088
Mielke, Alexander; Roubíček, Tomáš; Thomas, Marita
2012
Variational convergence of gradient flows and rate-independent evolutions in metric spaces. Zbl 1255.49078
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2012
A model for the evolution of laminates in finite-strain elastoplasticity. Zbl 1348.74060
Hackl, K.; Heinz, S.; Mielke, A.
2012
Emergence of rate-independent dissipation from viscous systems with wiggly energies. Zbl 1258.74169
Mielke, Alexander
2012
A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Zbl 1227.35161
Mielke, Alexander
2011
Differential, energetic, and metric formulations for rate-independent processes. Zbl 1251.35003
Mielke, Alexander
2011
Formulation of thermoelastic dissipative material behavior using GENERIC. Zbl 1272.74137
Mielke, Alexander
2011
Weighted energy-dissipation functionals for gradient flows. Zbl 1218.35007
Mielke, Alexander; Stefanelli, Ulisse
2011
Complete-damage evolution based on energies and stresses. Zbl 1209.74010
Mielke, Alexander
2011
An evolutionary elastoplastic plate model derived via $$\Gamma$$-convergence. Zbl 1232.35165
Liero, Matthias; Mielke, Alexander
2011
On thermodynamically consistent models and gradient structures for thermoplasticity. Zbl 1279.74008
Mielke, Alexander
2011
Damage of nonlinearly elastic materials at small strain – existence and regularity results. Zbl 1191.35159
Thomas, M.; Mielke, A.
2010
Complete damage in elastic and viscoelastic media and its energetics. Zbl 1227.74058
Mielke, Alexander; Roubíček, Tomáš; Zeman, Jan
2010
Crack growth in polyconvex materials. Zbl 1201.49013
Knees, Dorothee; Zanini, Chiara; Mielke, Alexander
2010
Error estimates for space-time discretizations of a rate-independent variational inequality. Zbl 1219.65059
Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse
2010
Dispersive stability of infinite-dimensional Hamiltonian systems on lattices. Zbl 1200.37071
Mielke, Alexander; Patz, Carsten
2010
High-frequency averaging in semi-classical Hartree-type equations. Zbl 1229.35261
Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof
2010
Modeling solutions with jumps for rate-independent systems on metric spaces. Zbl 1170.49036
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe
2009
Global existence for rate-independent gradient plasticity at finite strain. Zbl 1173.49013
Mainik, Andreas; Mielke, Alexander
2009
A complete-damage problem at small strains. Zbl 1238.74005
Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš
2009
Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003
Zelik, Sergey; Mielke, Alexander
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
2009
Numerical approaches to rate-independent processes and applications in inelasticity. Zbl 1166.74010
Mielke, Alexander; Roubíček, Tomáš
2009
Reverse approximation of energetic solutions to rate-independent processes. Zbl 1163.49030
Mielke, Alexander; Rindler, Filip
2009
$$\Gamma$$-limits and relaxations for rate-independent evolutionary problems. Zbl 1302.49013
Mielke, Alexander; Roubíček, Tomáš; Stefanelli, Ulisse
2008
On the inviscid limit of a model for crack propagation. Zbl 1151.49014
Knees, Dorothee; Mielke, Alexander; Zanini, Chiara
2008
A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043
Mielke, Alexander; Ortiz, Michael
2008
A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Zbl 1151.74319
Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse
2008
A metric approach to a class of doubly nonlinear evolution equations and applications. Zbl 1183.35164
Rossi, Riccarda; Mielke, Alexander; Savaré, Giuseppe
2008
Energy release rate for cracks in finite-strain elasticity. Zbl 1132.74038
Knees, Dorothee; Mielke, Alexander
2008
A discrete variational principle for rate-independent evolution. Zbl 1180.35283
Mielke, Alexander; Stefanelli, Ulisse
2008
Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Zbl 1185.35256
Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof
2008
Weak-convergence methods for Hamiltonian multiscale problems. Zbl 1144.35009
Mielke, Alexander
2008
Lagrangian and Hamiltonian two-scale reduction. Zbl 1152.81449
Giannoulis, Johannes; Herrmann, Michael; Mielke, Alexander
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.
2008
Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. Zbl 1185.35282
Mielke, Alexander; Timofte, Aida M.
2007
Existence and uniqueness results for a class of rate-independent hysteresis problems. Zbl 1121.34052
Mielke, Alexander; Rossi, Riccarda
2007
Thermally driven phase transformation in shape-memory alloys. Zbl 1138.49014
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.
2007
A model for temperature-induced phase transformations in finite-strain elasticity. Zbl 1128.74035
Mielke, Alexander
2007
Existence results for a class of rate-independent material models with nonconvex elastic energies. Zbl 1101.74015
Francfort, Gilles; Mielke, Alexander
2006
Rate-independent damage processes in nonlinear elasticity. Zbl 1094.35068
Mielke, Alexander; Roubíček, Tomáš
2006
On the rate-independent limit of systems with dry friction and small viscosity. Zbl 1109.74040
Efendiev, Messoud A.; Mielke, Alexander
2006
Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006
Mielke, Alexander; Müller, Stefan
2006
A rate-independent approach to the delamination problem. Zbl 1133.74038
Kočvara, Michal; Mielke, Alexander; Roubíček, Tomáš
2006
Macroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transforms. Zbl 1152.82024
Mielke, Alexander
2006
Micro-macro transition in the atomic chain via Whitham’s modulation equation. Zbl 1134.37362
Dreyer, W.; Herrmann, M.; Mielke, A.
2006
An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness. Zbl 1096.74017
Mielke, Alexander; Timofte, Aida M.
2006
Dispersive evolution of pulses in oscillator chains with general interaction potentials. Zbl 1152.34035
Giannoulis, Johannes; Mielke, Alexander
2006
A mathematical framework for generalized standard materials in the rate-independent case. Zbl 1298.74006
Mielke, Alexander
2006
Continuum descriptions for the dynamics in discrete lattices: derivation and justification. Zbl 1366.82036
Giannoulis, Johannes; Herrmann, Michael; Mielke, Alexander
2006
Analysis, modeling and simulation of multiscale problems. Zbl 1105.35002
2006
...and 79 more Documents
all top 5

### Cited by 1,776 Authors

 96 Mielke, Alexander 48 Schneider, Guido 47 Stefanelli, Ulisse 46 Roubíček, Tomáš 33 Rossi, Riccarda 28 Kružík, Martin 24 Neff, Patrizio 22 Scheel, Arnd 21 Mosler, Jörn 20 Peletier, Mark Adriaan 20 Valls Anglés, Cláudia 19 Hackl, Klaus 18 Savaré, Giuseppe 16 Barreira, Luis Manuel 16 Knees, Dorothee 16 Liero, Matthias 16 Mora, Maria Giovanna 15 Conti, Sergio 15 Thomas, Marita 14 Dal Maso, Gianni 14 Francfort, Gilles A. 14 Miehe, Christian 14 Zelik, Sergey V. 13 Lazzaroni, Giuliano 13 Marigo, Jean-Jacques 13 Ortiz, Michael 13 Uecker, Hannes 13 Zanini, Chiara 12 Deng, Shengfu 12 Groves, Mark D. 12 Li, Wuchen 12 Maas, Jan 11 Akagi, Goro 11 Bonetti, Elena 11 Düll, Wolf-Patrick 11 Heida, Martin 11 Negri, Matteo 11 Sandstede, Björn 10 Blömker, Dirk 10 Erbar, Matthias 10 Fellner, Klemens 10 Guo, Boling 10 Heinemann, Christian 10 Iooss, Gérard 10 James, Guillaume 10 Krejčí, Pavel 10 Solombrino, Francesco 10 Toader, Rodica 9 Carstensen, Carsten 9 Crismale, Vito 9 Herrmann, Michael 9 Il’ichev, Andreĭ Teĭmurazovich 9 Renger, D. R. Michiel 9 Zimmer, Johannes 8 Almi, Stefano 8 Benešová, Barbora 8 Bridges, Thomas J. 8 DeSimone, Antonio 8 Dondl, Patrick Werner 8 Gallay, Thierry 8 Gao, Hongjun 8 Giacomini, Alessandro 8 Hur, Vera Mikyoung 8 Junker, Philipp 8 Kochmann, Dennis M. 8 Kraus, Christiane 8 Kühn, Christian 8 Mantič, Vladislav 8 Mariano, Paolo Maria 8 Monsaingeon, Léonard 8 Neukamm, Stefan 8 Pelinovsky, Dmitry Efimovich 8 Schlichting, André 8 Tang, Bao Quoc 8 Wahlén, Erik 8 Zumbrun, Kevin R. 7 Bartels, Sören 7 Champneys, Alan R. 7 Davoli, Elisa 7 Dolzmann, Georg 7 Ghiba, Ionel-Dumitrel 7 Johnson, Mathew A. 7 Jüngel, Ansgar 7 Khludnev, Aleksandr Mikhaĭlovich 7 Lerman, Lev 7 Lloyd, David J. B. 7 Martin, Robert J. 7 Müller, Stefan 7 Nicholls, David P. 7 Schmitzer, Bernhard 7 Svendsen, Bob 7 Visintin, Augusto 7 Vorotnikov, Dmitry A. 7 Yanchuk, Sergiĭ Volodymyrovych 6 Alessi, Roberto 6 Auricchio, Ferdinando 6 Babadjian, Jean-François 6 Bonfanti, Giovanna 6 Dohnal, Tomáš 6 Duan, Jinqiao ...and 1,676 more Authors
all top 5

### Cited in 256 Serials

 101 Archive for Rational Mechanics and Analysis 96 Journal of Differential Equations 67 Physica D 52 Computer Methods in Applied Mechanics and Engineering 51 Continuum Mechanics and Thermodynamics 48 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 44 Journal of Nonlinear Science 40 Journal of the Mechanics and Physics of Solids 40 SIAM Journal on Mathematical Analysis 40 Calculus of Variations and Partial Differential Equations 35 ZAMP. Zeitschrift für angewandte Mathematik und Physik 34 Journal of Dynamics and Differential Equations 34 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 34 Discrete and Continuous Dynamical Systems. Series S 33 Journal of Mathematical Analysis and Applications 31 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 31 Journal of Elasticity 27 Communications in Mathematical Physics 26 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 25 Discrete and Continuous Dynamical Systems 23 Mathematical Methods in the Applied Sciences 20 Journal of Statistical Physics 18 Journal of Functional Analysis 18 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 18 Mathematics and Mechanics of Solids 16 International Journal for Numerical Methods in Engineering 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 16 NoDEA. Nonlinear Differential Equations and Applications 16 Chaos 16 GAMM-Mitteilungen 15 Nonlinear Analysis. Real World Applications 14 Nonlinearity 13 Applicable Analysis 13 Computational Mechanics 13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 13 Journal of Evolution Equations 12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 11 SIAM Journal on Applied Dynamical Systems 10 International Journal of Engineering Science 10 Journal of Mathematical Physics 10 Communications in Nonlinear Science and Numerical Simulation 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 9 Meccanica 9 Transactions of the American Mathematical Society 9 European Journal of Applied Mathematics 9 European Journal of Mechanics. A. Solids 8 International Journal of Plasticity 8 Wave Motion 8 Journal of Computational and Applied Mathematics 8 Communications in Partial Differential Equations 8 European Journal of Mechanics. B. Fluids 8 Discrete and Continuous Dynamical Systems. Series B 8 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 7 Journal of Computational Physics 7 Journal of Fluid Mechanics 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Journal of Mathematical Sciences (New York) 7 Communications on Pure and Applied Analysis 7 Advances in Calculus of Variations 6 Acta Mechanica 6 Applied Mathematics and Optimization 6 Mathematische Nachrichten 6 Chinese Annals of Mathematics. Series B 6 Asymptotic Analysis 6 SIAM Journal on Applied Mathematics 6 Nonlinear Dynamics 5 Communications on Pure and Applied Mathematics 5 Quarterly of Applied Mathematics 5 Applied Mathematics Letters 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 5 Stochastic Processes and their Applications 5 Journal of Convex Analysis 5 Multiscale Modeling & Simulation 4 Computers & Mathematics with Applications 4 International Journal of Solids and Structures 4 Journal of Engineering Mathematics 4 Physica A 4 The Annals of Probability 4 Applied Mathematics and Computation 4 Inventiones Mathematicae 4 Journal of Optimization Theory and Applications 4 Numerische Mathematik 4 Studies in Applied Mathematics 4 Acta Applicandae Mathematicae 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. Series A. 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 SIAM Journal on Imaging Sciences 4 Kinetic and Related Models 3 Theoretical and Mathematical Physics 3 Mathematics of Computation 3 Chaos, Solitons and Fractals 3 Advances in Mathematics 3 Integral Equations and Operator Theory ...and 156 more Serials
all top 5

### Cited in 47 Fields

 933 Partial differential equations (35-XX) 703 Mechanics of deformable solids (74-XX) 311 Calculus of variations and optimal control; optimization (49-XX) 261 Dynamical systems and ergodic theory (37-XX) 218 Fluid mechanics (76-XX) 155 Ordinary differential equations (34-XX) 132 Statistical mechanics, structure of matter (82-XX) 122 Numerical analysis (65-XX) 113 Probability theory and stochastic processes (60-XX) 95 Operator theory (47-XX) 70 Mechanics of particles and systems (70-XX) 57 Classical thermodynamics, heat transfer (80-XX) 46 Global analysis, analysis on manifolds (58-XX) 45 Biology and other natural sciences (92-XX) 42 Optics, electromagnetic theory (78-XX) 38 Differential geometry (53-XX) 26 Quantum theory (81-XX) 25 Measure and integration (28-XX) 25 Functional analysis (46-XX) 24 Operations research, mathematical programming (90-XX) 18 Difference and functional equations (39-XX) 15 Real functions (26-XX) 13 Systems theory; control (93-XX) 10 Computer science (68-XX) 10 Information and communication theory, circuits (94-XX) 9 Geophysics (86-XX) 8 Combinatorics (05-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Integral equations (45-XX) 7 General topology (54-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 General and overarching topics; collections (00-XX) 6 Statistics (62-XX) 5 Functions of a complex variable (30-XX) 4 Approximations and expansions (41-XX) 3 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Sequences, series, summability (40-XX) 2 Geometry (51-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 Integral transforms, operational calculus (44-XX)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.