Edit Profile (opens in new tab) Beauchard, Karine Co-Author Distance Author ID: beauchard.karine Published as: Beauchard, Karine; Beauchard, K. Homepage: http://www.cmls.polytechnique.fr/perso/beauchard/ External Links: MGP · ORCID · Wikidata · dblp · IdRef · theses.fr Documents Indexed: 43 Publications since 2005, including 1 Additional arXiv Preprint 1 Contribution as Editor Co-Authors: 32 Co-Authors with 37 Joint Publications 1,134 Co-Co-Authors all top 5 Co-Authors 7 single-authored 5 Coron, Jean-Michel 5 Marbach, Frédéric 5 Rouchon, Pierre 4 Cannarsa, Piermarco 4 Pravda-Starov, Karel 3 Laurent, Camille 3 Teismann, Holger 2 Le Borgne, Jérémy 2 Mirrahimi, Mazyar 2 Morancey, Morgan 2 Pereira da Silva, Paulo Sérgio 2 Zuazua, Enrique 1 Alouges, François 1 Chitour, Yacine 1 Dardé, Jérémi 1 Egidi, Michela 1 Ervedoza, Sylvain 1 Guglielmi, Roberto 1 Helffer, Bernard 1 Henry, Raphaël 1 Jaming, Philippe 1 Kateb, Djalil M. 1 Koenig, Armand 1 Lange, Horst 1 Le Balc’h, Kévin 1 Long, Ruixing 1 Miller, Luc 1 Nersesyan, Vahagn 1 Robbiano, Luc 1 Trélat, Emmanuel 1 Yamamoto, Masahiro 1 Zarrouati-Vissière, Nadège all top 5 Serials 4 Journal of Differential Equations 4 SIAM Journal on Control and Optimization 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal de l’École Polytechnique – Mathématiques 2 Automatica 2 Journal of Functional Analysis 2 Systems & Control Letters 2 MCSS. Mathematics of Control, Signals, and Systems 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 Studia Mathematica 1 Annales de l’Institut Fourier 1 Journal of Algebra 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Séminaire Équations aux Dérivées Partielles 1 Journal of the European Mathematical Society (JEMS) 1 Mathematical Control and Related Fields 1 Séminaire Laurent Schwartz. EDP et Applications all top 5 Fields 37 Systems theory; control (93-XX) 31 Partial differential equations (35-XX) 9 Quantum theory (81-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 39 Publications have been cited 743 times in 382 Documents Cited by ▼ Year ▼ Large time asymptotics for partially dissipative hyperbolic systems. Zbl 1237.35017 Beauchard, Karine; Zuazua, Enrique 73 2011 Local controllability of a 1-D Schrödinger equation. Zbl 1124.93009 Beauchard, Karine 67 2005 Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control. Zbl 1202.35332 Beauchard, Karine; Laurent, Camille 64 2010 Controllability of a quantum particle in a moving potential well. Zbl 1188.93017 Beauchard, Karine; Coron, Jean-Michel 63 2006 Null controllability of Grushin-type operators in dimension two. Zbl 1293.35148 Beauchard, Karine; Cannarsa, Piermarco; Guglielmi, Roberto 51 2014 Null-controllability of hypoelliptic quadratic differential equations. Zbl 1403.93041 Beauchard, Karine; Pravda-Starov, Karel 34 2018 Controllability issues for continuous-spectrum systems and ensemble controllability of Bloch equations. Zbl 1193.93073 Beauchard, Karine; Coron, Jean-Michel; Rouchon, Pierre 27 2010 Implicit Lyapunov control of finite dimensional Schrödinger equations. Zbl 1110.81063 Beauchard, Karine; Coron, Jean Michel; Mirrahimi, Mazyar; Rouchon, Pierre 26 2007 Some controllability results for the 2D Kolmogorov equation. Zbl 1172.93005 Beauchard, K.; Zuazua, E. 24 2009 Practical stabilization of a quantum particle in a one-dimensional infinite square potential well. Zbl 1194.93176 Beauchard, Karine; Mirrahimi, Mazyar 23 2009 Degenerate parabolic operators of Kolmogorov type with a geometric control condition. Zbl 1311.93042 Beauchard, Karine; Helffer, Bernard; Henry, Raphael; Robbiano, Luc 22 2015 Local controllability and non-controllability for a 1D wave equation with bilinear control. Zbl 1221.35221 Beauchard, Karine 20 2011 Null controllability of Kolmogorov-type equations. Zbl 1291.93035 Beauchard, K. 19 2014 2d Grushin-type equations: minimal time and null controllable data. Zbl 1321.35098 Beauchard, Karine; Miller, Luc; Morancey, Morgan 19 2015 Heat equation on the Heisenberg group: observability and applications. Zbl 1366.35206 Beauchard, K.; Cannarsa, P. 18 2017 Controllablity of a quantum particle in a 1D variable domain. Zbl 1132.35446 Beauchard, Karine 17 2008 Minimal time issues for the observability of Grushin-type equations. (Sur le temps minimal pour l’observabilité d’équations de type Grushin.) Zbl 1448.35316 Beauchard, Karine; Dardé, Jérémi; Ervedoza, Sylvain 16 2020 Inverse source problem and null controllability for multidimensional parabolic operators of Grushin type. Zbl 1286.35260 Beauchard, K.; Cannarsa, P.; Yamamoto, M. 15 2014 Local controllability of a one-dimensional beam equation. Zbl 1172.35325 Beauchard, Karine 14 2008 Local controllability of 1D Schrödinger equations with bilinear control and minimal time. Zbl 1281.93016 Beauchard, Karine; Morancey, Morgan 14 2014 Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations. Zbl 1467.93030 Beauchard, Karine; Jaming, Philippe; Pravda-Starov, Karel 12 2021 Magnetization switching on small ferromagnetic ellipsoidal samples. Zbl 1167.49003 Alouges, François; Beauchard, Karine 11 2009 Quadratic obstructions to small-time local controllability for scalar-input systems. Zbl 1377.93042 Beauchard, Karine; Marbach, Frédéric 11 2018 Semi-global weak stabilization of bilinear Schrödinger equations. (Stabilisation faible semi-globale d’équations de Schrödinger bilinéaires.) Zbl 1205.35051 Beauchard, Karine; Nersesyan, Vahagn 11 2010 Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports. Zbl 1451.93021 Beauchard, Karine; Egidi, Michela; Pravda-Starov, Karel 10 2020 Null-controllability of non-autonomous Ornstein-Uhlenbeck equations. Zbl 1480.93035 Beauchard, Karine; Pravda-Starov, Karel 9 2017 Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations. Zbl 1436.93018 Beauchard, Karine; Marbach, Frédéric 8 2020 Stabilization for an ensemble of half-spin systems. Zbl 1244.93134 Beauchard, Karine; Pereira Da Silva, Paulo Sérgio; Rouchon, Pierre 7 2012 Spectral controllability for 2D and 3D linear Schrödinger equations. Zbl 1191.35222 Beauchard, K.; Chitour, Y.; Kateb, D.; Long, R. 6 2009 Minimal time for the bilinear control of Schrödinger equations. Zbl 1296.93076 Beauchard, Karine; Coron, Jean-Michel; Teismann, Holger 6 2014 Local exact controllability of a one-dimensional nonlinear Schrödinger equation. Zbl 1326.35330 Beauchard, Karine; Lange, Horst; Teismann, Holger 6 2015 Minimal time for the approximate bilinear control of Schrödinger equations. Zbl 1391.93036 Beauchard, Karine; Coron, Jean-Michel; Teismann, Holger 5 2018 Bilinear control of high frequencies for a 1D Schrödinger equation. Zbl 1368.81085 Beauchard, K.; Laurent, C. 5 2017 Null-controllability of linear parabolic-transport systems. (Contrôlabilité à zéro des systèmes paraboliques-transport linéaires couplés.) Zbl 1443.93030 Beauchard, Karine; Koenig, Armand; Le Balc’h, Kévin 4 2020 Local exact controllability of the \(2D\)-Schrödinger-Poisson system. Zbl 1375.35419 Beauchard, Karine; Laurent, Camille 2 2017 Inverse coefficient problem for Grushin-type parabolic operators. Zbl 1394.35575 Beauchard, Karine; Cannarsa, Piermarco 1 2014 Stabilization of an arbitrary profile for an ensemble of half-spin systems. Zbl 1364.93619 Beauchard, Karine; Pereira da Silva, Paulo Sérgio; Rouchon, Pierre 1 2013 On expansions for nonlinear systems error estimates and convergence issues. Zbl 1516.34026 Beauchard, Karine; Le Borgne, Jérémy; Marbach, Frédéric 1 2023 Growth of structure constants of free Lie algebras relative to Hall bases. Zbl 07596234 Beauchard, Karine; Le Borgne, Jérémy; Marbach, Frédéric 1 2022 On expansions for nonlinear systems error estimates and convergence issues. Zbl 1516.34026 Beauchard, Karine; Le Borgne, Jérémy; Marbach, Frédéric 1 2023 Growth of structure constants of free Lie algebras relative to Hall bases. Zbl 07596234 Beauchard, Karine; Le Borgne, Jérémy; Marbach, Frédéric 1 2022 Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations. Zbl 1467.93030 Beauchard, Karine; Jaming, Philippe; Pravda-Starov, Karel 12 2021 Minimal time issues for the observability of Grushin-type equations. (Sur le temps minimal pour l’observabilité d’équations de type Grushin.) Zbl 1448.35316 Beauchard, Karine; Dardé, Jérémi; Ervedoza, Sylvain 16 2020 Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports. Zbl 1451.93021 Beauchard, Karine; Egidi, Michela; Pravda-Starov, Karel 10 2020 Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations. Zbl 1436.93018 Beauchard, Karine; Marbach, Frédéric 8 2020 Null-controllability of linear parabolic-transport systems. (Contrôlabilité à zéro des systèmes paraboliques-transport linéaires couplés.) Zbl 1443.93030 Beauchard, Karine; Koenig, Armand; Le Balc’h, Kévin 4 2020 Null-controllability of hypoelliptic quadratic differential equations. Zbl 1403.93041 Beauchard, Karine; Pravda-Starov, Karel 34 2018 Quadratic obstructions to small-time local controllability for scalar-input systems. Zbl 1377.93042 Beauchard, Karine; Marbach, Frédéric 11 2018 Minimal time for the approximate bilinear control of Schrödinger equations. Zbl 1391.93036 Beauchard, Karine; Coron, Jean-Michel; Teismann, Holger 5 2018 Heat equation on the Heisenberg group: observability and applications. Zbl 1366.35206 Beauchard, K.; Cannarsa, P. 18 2017 Null-controllability of non-autonomous Ornstein-Uhlenbeck equations. Zbl 1480.93035 Beauchard, Karine; Pravda-Starov, Karel 9 2017 Bilinear control of high frequencies for a 1D Schrödinger equation. Zbl 1368.81085 Beauchard, K.; Laurent, C. 5 2017 Local exact controllability of the \(2D\)-Schrödinger-Poisson system. Zbl 1375.35419 Beauchard, Karine; Laurent, Camille 2 2017 Degenerate parabolic operators of Kolmogorov type with a geometric control condition. Zbl 1311.93042 Beauchard, Karine; Helffer, Bernard; Henry, Raphael; Robbiano, Luc 22 2015 2d Grushin-type equations: minimal time and null controllable data. Zbl 1321.35098 Beauchard, Karine; Miller, Luc; Morancey, Morgan 19 2015 Local exact controllability of a one-dimensional nonlinear Schrödinger equation. Zbl 1326.35330 Beauchard, Karine; Lange, Horst; Teismann, Holger 6 2015 Null controllability of Grushin-type operators in dimension two. Zbl 1293.35148 Beauchard, Karine; Cannarsa, Piermarco; Guglielmi, Roberto 51 2014 Null controllability of Kolmogorov-type equations. Zbl 1291.93035 Beauchard, K. 19 2014 Inverse source problem and null controllability for multidimensional parabolic operators of Grushin type. Zbl 1286.35260 Beauchard, K.; Cannarsa, P.; Yamamoto, M. 15 2014 Local controllability of 1D Schrödinger equations with bilinear control and minimal time. Zbl 1281.93016 Beauchard, Karine; Morancey, Morgan 14 2014 Minimal time for the bilinear control of Schrödinger equations. Zbl 1296.93076 Beauchard, Karine; Coron, Jean-Michel; Teismann, Holger 6 2014 Inverse coefficient problem for Grushin-type parabolic operators. Zbl 1394.35575 Beauchard, Karine; Cannarsa, Piermarco 1 2014 Stabilization of an arbitrary profile for an ensemble of half-spin systems. Zbl 1364.93619 Beauchard, Karine; Pereira da Silva, Paulo Sérgio; Rouchon, Pierre 1 2013 Stabilization for an ensemble of half-spin systems. Zbl 1244.93134 Beauchard, Karine; Pereira Da Silva, Paulo Sérgio; Rouchon, Pierre 7 2012 Large time asymptotics for partially dissipative hyperbolic systems. Zbl 1237.35017 Beauchard, Karine; Zuazua, Enrique 73 2011 Local controllability and non-controllability for a 1D wave equation with bilinear control. Zbl 1221.35221 Beauchard, Karine 20 2011 Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control. Zbl 1202.35332 Beauchard, Karine; Laurent, Camille 64 2010 Controllability issues for continuous-spectrum systems and ensemble controllability of Bloch equations. Zbl 1193.93073 Beauchard, Karine; Coron, Jean-Michel; Rouchon, Pierre 27 2010 Semi-global weak stabilization of bilinear Schrödinger equations. (Stabilisation faible semi-globale d’équations de Schrödinger bilinéaires.) Zbl 1205.35051 Beauchard, Karine; Nersesyan, Vahagn 11 2010 Some controllability results for the 2D Kolmogorov equation. Zbl 1172.93005 Beauchard, K.; Zuazua, E. 24 2009 Practical stabilization of a quantum particle in a one-dimensional infinite square potential well. Zbl 1194.93176 Beauchard, Karine; Mirrahimi, Mazyar 23 2009 Magnetization switching on small ferromagnetic ellipsoidal samples. Zbl 1167.49003 Alouges, François; Beauchard, Karine 11 2009 Spectral controllability for 2D and 3D linear Schrödinger equations. Zbl 1191.35222 Beauchard, K.; Chitour, Y.; Kateb, D.; Long, R. 6 2009 Controllablity of a quantum particle in a 1D variable domain. Zbl 1132.35446 Beauchard, Karine 17 2008 Local controllability of a one-dimensional beam equation. Zbl 1172.35325 Beauchard, Karine 14 2008 Implicit Lyapunov control of finite dimensional Schrödinger equations. Zbl 1110.81063 Beauchard, Karine; Coron, Jean Michel; Mirrahimi, Mazyar; Rouchon, Pierre 26 2007 Controllability of a quantum particle in a moving potential well. Zbl 1188.93017 Beauchard, Karine; Coron, Jean-Michel 63 2006 Local controllability of a 1-D Schrödinger equation. Zbl 1124.93009 Beauchard, Karine 67 2005 all cited Publications top 5 cited Publications all top 5 Cited by 436 Authors 30 Beauchard, Karine 15 Cannarsa, Piermarco 12 Morancey, Morgan 11 Sigalotti, Mario 10 Boscain, Ugo 10 Coron, Jean-Michel 8 Duca, Alessandro 7 Chambrion, Thomas 7 Crin-Barat, Timothée 7 Laurent, Camille 7 Martinez, Patrick 7 Ouzahra, Mohamed 7 Rouchon, Pierre 7 Seelmann, Albrecht 7 Tautenhahn, Martin 7 Veselić, Ivan 7 Zuazua, Enrique 6 Ervedoza, Sylvain 6 Nersesyan, Vahagn 6 Pravda-Starov, Karel 6 Salomon, Julien 6 Xiang, Shengquan 5 Cong, Shuang 5 Danchin, Raphaël 5 Feng, Binhua 5 Koenig, Armand 5 Kuang, Sen 5 Qu, Peng 5 Rosier, Lionel 5 Urbani, Cristina 5 Vancostenoble, Judith 5 Zhao, Dun 4 Alphonse, Paul 4 Caponigro, Marco 4 Dardé, Jérémi 4 Dicke, Alexander 4 Ducomet, Bernard 4 Egidi, Michela 4 Fragnelli, Genni 4 Geshkovski, Borjan 4 Helffer, Bernard 4 Léautaud, Matthieu 4 Li, Jr-Shin 4 Lissy, Pierre 4 Marbach, Frédéric 4 Peng, Yuejun 4 Pozzoli, Eugenio 4 Prohl, Andreas 4 Said-Houari, Belkacem 4 Seifert, Christian 4 Trélat, Emmanuel 4 Ueda, Yoshihiro 3 Augier, Nicolas 3 Bedrossian, Jacob 3 Bianchini, Roberta 3 Blanc, Xavier 3 Borzì, Alfio 3 Bournissou, Mégane 3 Boyer, Franck 3 Cung The Anh 3 Dubey, Shruti A. 3 Dwivedi, Sharad 3 Gagnon, Ludovick 3 Gallaun, Dennis 3 Giovangigli, Vincent 3 Grebenkov, Denis S. 3 Henry, Raphaël 3 Kawashima, Shuichi 3 Klar, Axel 3 Le Balc’h, Kévin 3 Letrouit, Cyril 3 Liu, Cunming 3 Majee, Ananta K. 3 Majumdar, Subrata 3 Mason, Paolo 3 Mirrahimi, Mazyar 3 Moyano, Iván 3 Natalini, Roberto 3 Nečasová, Šárka 3 Pereira da Silva, Paulo Sérgio 3 Puel, Jean-Pierre 3 Sun, Chenmin 3 Teismann, Holger 3 Tran, Minh-Binh 3 Tse, Oliver 3 Wang, Gengsheng 3 Wang, Ming 3 Zerrik, El Hassan 3 Zhang, Bingyu 2 Agrachev, Andreĭ Aleksandrovich 2 Ahamed, Sakil 2 Alabau-Boussouira, Fatiha 2 Almog, Yaniv 2 Ammari, Kais 2 Atifi, Khalid 2 Balachandran, Krishnan 2 Baldi, Pietro 2 Balmaseda, Aitor 2 Barani Balan, Natesan 2 Baudouin, Lucie ...and 336 more Authors all top 5 Cited in 119 Serials 31 Journal of Differential Equations 26 SIAM Journal on Control and Optimization 24 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 17 Journal de Mathématiques Pures et Appliquées. Neuvième Série 12 Automatica 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 SIAM Journal on Mathematical Analysis 10 Mathematical Control and Related Fields 8 Journal of Mathematical Analysis and Applications 8 Systems & Control Letters 8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 International Journal of Control 6 Communications in Mathematical Physics 6 Mathematical Methods in the Applied Sciences 6 Journal of Functional Analysis 6 Journal de l’École Polytechnique – Mathématiques 6 Séminaire Laurent Schwartz. EDP et Applications 5 Archive for Rational Mechanics and Analysis 5 European Journal of Control 5 Journal of Evolution Equations 4 Archiv der Mathematik 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 MCSS. Mathematics of Control, Signals, and Systems 4 Journal of Scientific Computing 4 Communications in Partial Differential Equations 3 Journal of the Franklin Institute 3 Journal of Mathematical Physics 3 Memoirs of the American Mathematical Society 3 NoDEA. Nonlinear Differential Equations and Applications 3 Nonlinear Analysis. Real World Applications 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Systems Science and Complexity 3 Journal of the Institute of Mathematics of Jussieu 3 Discrete and Continuous Dynamical Systems. Series S 3 Analysis & PDE 3 Evolution Equations and Control Theory 3 Advances in Nonlinear Analysis 2 Applicable Analysis 2 Physics Letters. A 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annales de l’Institut Fourier 2 Proceedings of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 Chinese Annals of Mathematics. Series B 2 Journal of Inverse and Ill-Posed Problems 2 New Journal of Physics 2 Journal of the European Mathematical Society (JEMS) 2 Communications on Pure and Applied Analysis 2 Journal of Hyperbolic Differential Equations 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Journal of Physics A: Mathematical and Theoretical 2 AIMS Mathematics 2 Pure and Applied Analysis 2 Annales Henri Lebesgue 1 Journal of Computational Physics 1 Nonlinearity 1 Physics Letters. B 1 Studia Mathematica 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Applied Mathematics and Optimization 1 Journal of Optimization Theory and Applications 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Physica D 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Probability Theory and Related Fields 1 Constructive Approximation 1 Applied Mathematical Modelling 1 SIAM Journal on Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 International Journal of Robust and Nonlinear Control 1 Topological Methods in Nonlinear Analysis 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Sciences (New York) 1 Turkish Journal of Mathematics 1 Bulletin des Sciences Mathématiques 1 Advances in Computational Mathematics 1 Opuscula Mathematica 1 Advances in Differential Equations 1 The Journal of Fourier Analysis and Applications 1 Mathematical Problems in Engineering 1 Differential Equations and Dynamical Systems 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Revista Matemática Complutense 1 Journal of Mathematical Fluid Mechanics 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Dynamical and Control Systems 1 Communications in Contemporary Mathematics 1 Annales Henri Poincaré 1 Qualitative Theory of Dynamical Systems 1 Journal of Applied Mathematics 1 Portugaliae Mathematica. Nova Série 1 Quantum Information Processing ...and 19 more Serials all top 5 Cited in 38 Fields 293 Partial differential equations (35-XX) 226 Systems theory; control (93-XX) 59 Quantum theory (81-XX) 35 Fluid mechanics (76-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 22 Operator theory (47-XX) 22 Numerical analysis (65-XX) 15 Statistical mechanics, structure of matter (82-XX) 10 Probability theory and stochastic processes (60-XX) 10 Mechanics of deformable solids (74-XX) 8 Special functions (33-XX) 8 Ordinary differential equations (34-XX) 8 Biology and other natural sciences (92-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Mechanics of particles and systems (70-XX) 6 Optics, electromagnetic theory (78-XX) 5 Real functions (26-XX) 5 Functions of a complex variable (30-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Functional analysis (46-XX) 4 Operations research, mathematical programming (90-XX) 3 Combinatorics (05-XX) 3 Approximations and expansions (41-XX) 3 Differential geometry (53-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Topological groups, Lie groups (22-XX) 2 Integral equations (45-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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