## Zuazua, Enrique

Compute Distance To:
 Author ID: zuazua.enrique Published as: Zuazua, Enrique; Zuazua, E.; Zuazua, Enrike more...less Homepage: http://verso.mat.uam.es/web/ezuazua/zuazua.html External Links: MGP · Wikidata · dblp · IdRef · theses.fr
 Documents Indexed: 357 Publications since 1987, including 3 Books 9 Contributions as Editor · 1 Further Contribution Biographic References: 4 Publications Co-Authors: 155 Co-Authors with 309 Joint Publications 3,533 Co-Co-Authors
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### Co-Authors

 51 single-authored 21 Trélat, Emmanuel 18 Zhang, Xu 17 Castro, Carlos 12 Escobedo Martínez, Miguel 12 Perla Menzala, Gustavo Alberto 11 Micu, Sorin 10 Ervedoza, Sylvain 10 Marica, Aurora 9 Ignat, Liviu I. 9 Puel, Jean-Pierre 8 Fernández-Cara, Enrique 8 Privat, Yannick 7 Biccari, Umberto 7 Cioranescu, Doina 7 Donato, Patrizia 7 Vazquez, Juan Luis 6 Lions, Jacques-Louis 5 Dáger, René 5 Fabre, Caroline 5 Lebeau, Gilles 5 Lohéac, Jérôme 5 Lopez, Antonio M. jun. 5 Lü, Qi 5 Negreanu, Mihaela 5 Ortega, Jaime H. 5 Tucsnak, Marius 4 de Teresa, Luz 4 Porretta, Alessio 4 Warma, Mahamadi 3 Aguirre Estibalez, Julián 3 Araruna, Fágner Dias 3 Chenais, Denise 3 Duro, Gema 3 Gugat, Martin 3 Ko, Dongnam 3 Komornik, Vilmos 3 Lazar, Martin 3 Orive Illera, Rafael 3 Pighin, Dario 3 Pozo, Alejandro 3 Ruiz-Balet, Domènec 3 Zheng, Chuang 2 Allahverdi, Navid 2 Arrieta, José M. 2 Beauchard, Karine 2 Braz e Silva, Pablo 2 Casas, Eduardo 2 Chaves-Silva, Felipe Wallison 2 Conca, Carlos 2 de Figueiredo, Isabel Maria Narra 2 de León Rodríguez, Manuel 2 Feireisl, Eduard 2 Fernández, Luis Alberto 2 Geshkovski, Borjan 2 Gosse, Laurent 2 Han, Zhongjie 2 Haraux, Alain 2 Hernández-Santamaría, Víctor 2 Infante, Juan-Antonio 2 Jaffard, Stéphane 2 Krejčiřík, David 2 Lance, Gontran 2 Lecaros, Rodrigo 2 Lissy, Pierre 2 López-Fernández, María 2 Macià, Fabricio 2 Maity, Debayan 2 Palacios, Francisco 2 Pazoto, Ademir Fernando 2 Rauch, Jeffrey B. 2 Rodríguez-Bernal, Aníbal 2 Tcheugoué Tébou, Louis Roder 2 Vancostenoble, Judith 2 Wang, Gengsheng 1 Affili, Elisa 1 Andradas, Carlos 1 Bárcena-Petisco, Jon Asier 1 Bardos, Claude Williams 1 Beli, Constantin-Nicolae 1 Bianchini, Roberta 1 Bisognin, Eleni 1 Bisognin, Vanilde 1 Cabanillas, Victor R. 1 Casado-Díaz, Juan 1 Cazacu, Cristian M. 1 Cazenave, Thierry 1 Cea, Miguel 1 Choulli, Mourad 1 Ciepliński, Krzysztof 1 Cordero, Luis A. 1 Cortés López, Juan Carlos 1 De Menezes, Silvano Bezerra 1 Dehman, Belhassen 1 DeVore, Ronald A. 1 Doubova, Anna 1 Duoandikoetxea, Javier 1 Dutykh, Denys 1 Duyckaerts, Thomas 1 Ersoy, Mehmet 1 Esteve-Yagüe, Carlos ...and 56 more Co-Authors
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### Serials

 27 Comptes Rendus de l’Académie des Sciences. Série I 21 SIAM Journal on Control and Optimization 20 Journal de Mathématiques Pures et Appliquées. Neuvième Série 16 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Journal of Differential Equations 10 Archive for Rational Mechanics and Analysis 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Systems & Control Letters 9 Asymptotic Analysis 9 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 Numerische Mathematik 7 Communications in Partial Differential Equations 6 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 5 Mathematics of Computation 5 Journal of Optimization Theory and Applications 5 SIAM Journal on Mathematical Analysis 5 Discrete and Continuous Dynamical Systems 4 Automatica 4 Journal of Functional Analysis 4 Mathematical Control and Related Fields 3 Control and Cybernetics 3 SIAM Journal on Numerical Analysis 3 Differential and Integral Equations 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Computational and Applied Mathematics 3 Advances in Differential Equations 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 3 Journal of the European Mathematical Society (JEMS) 3 Multiscale Modeling & Simulation 2 Nonlinearity 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Indiana University Mathematics Journal 2 Quarterly of Applied Mathematics 2 Transactions of the American Mathematical Society 2 Chinese Annals of Mathematics. Series B 2 Applied Mathematics Letters 2 The Journal of Fourier Analysis and Applications 2 Matemática Contemporânea 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Communications in Contemporary Mathematics 2 La Gaceta de la Real Sociedad Matemática Española 2 Foundations of Computational Mathematics 2 Discrete and Continuous Dynamical Systems. Series B 2 Advanced Nonlinear Studies 2 Communications on Pure and Applied Analysis 2 Networks and Heterogeneous Media 2 SpringerBriefs in Mathematics 1 Houston Journal of Mathematics 1 IMA Journal of Applied Mathematics 1 IMA Journal of Numerical Analysis 1 Inverse Problems 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Mathematische Annalen 1 Portugaliae Mathematica 1 Ricerche di Matematica 1 Optimal Control Applications & Methods 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Mathematical and Computer Modelling 1 MCSS. Mathematics of Control, Signals, and Systems 1 Revista Matemática de la Universidad Complutense de Madrid 1 European Journal of Applied Mathematics 1 Acta Mathematica Universitatis Comenianae. New Series 1 Journal of Elasticity 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Calculus of Variations and Partial Differential Equations 1 Séminaire Équations aux Dérivées Partielles 1 Advances in Computational Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Evolution Equations 1 Journal of Systems Science and Complexity 1 Portugaliae Mathematica. Nova Série 1 Cubo Matemática Educacional 1 Oberwolfach Reports 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Mathématiques & Applications (Berlin) 1 Publicaciones de la Real Sociedad Matemática Española 1 Proceedings of the Estonian Academy of Sciences 1 Matapli 1 Nonlinear Analysis. Theory, Methods & Applications 1 Pure and Applied Functional Analysis 1 IEEE Control Systems
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### Fields

 266 Partial differential equations (35-XX) 198 Systems theory; control (93-XX) 66 Mechanics of deformable solids (74-XX) 64 Calculus of variations and optimal control; optimization (49-XX) 53 Numerical analysis (65-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 10 Fluid mechanics (76-XX) 7 Ordinary differential equations (34-XX) 7 Operator theory (47-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Operations research, mathematical programming (90-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 4 Biology and other natural sciences (92-XX) 3 Real functions (26-XX) 3 Integral equations (45-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

320 Publications have been cited 6,075 times in 3,107 Documents Cited by Year
Exponential decay for the semilinear wave equation with locally distributed damping. Zbl 0716.35010
Zuazua, Enrike
1990
The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential. Zbl 0953.35053
Vazquez, Juan Luis; Zuazua, Enrike
2000
Approximate controllability of the semilinear heat equation. Zbl 0818.93032
Fabre, Caroline; Puel, Jean-Pierre; Zuazua, Enrike
1995
Null and approximate controllability for weakly blowing up semilinear heat equations. Zbl 0970.93023
Fernández-Cara, Enrique; Zuazua, Enrique
2000
A direct method for the boundary stabilization of the wave equation. Zbl 0636.93064
Komornik, Vilmos; Zuazua, Enrike
1990
The cost of approximate controllability for heat equations: The linear case. Zbl 1007.93034
Fernández-Cara, Enrique; Zuazua, Enrique
2000
Propagation, observation, and control of waves approximated by finite difference methods. Zbl 1077.65095
Zuazua, Enrique
2005
Controllability and observability of partial differential equations: some results and open problems. Zbl 1193.35234
Zuazua, Enrique
2007
Large time behavior for convection-diffusion equations in $$\mathbb{R}{} ^ N$$. Zbl 0762.35011
Escobedo, Miguel; Zuazua, Enrike
1991
Decay estimates for some semilinear damped hyperbolic problems. Zbl 0654.35070
Haraux, A.; Zuazua, E.
1988
Uniform stabilization of the wave equation by nonlinear boundary feedback. Zbl 0695.93090
Zuazua, Enrike
1990
Wave propagation, observation and control in 1-$$d$$ flexible multi-structures. Zbl 1083.74002
Dáger, René; Zuazua, Enrique
2006
On the controllability of parabolic systems with a nonlinear term involving the state and the gradient. Zbl 1038.93041
Doubova, A.; Fernández-Cara, E.; González-Burgos, M.; Zuazua, E.
2002
The rate at which energy decays in a damped string. Zbl 0818.35072
Cox, Steven; Zuazua, Enrique
1994
Null-controllability of a system of linear thermoelasticity. Zbl 1064.93501
Lebeau, Gilles; Zuazua, Enrique
1998
On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials. Zbl 1248.93031
Duyckaerts, Thomas; Zhang, Xu; Zuazua, Enrique
2008
Exact controllability for semilinear wave equations in one space dimension. Zbl 0769.93017
Zuazua, E.
1993
Decay rates for the three-dimensional linear system of thermoelasticity. Zbl 0939.74016
Lebeau, Gilles; Zuazua, Enrique
1999
Boundary observability for the space semi-discretizations of the 1-D wave equation. Zbl 0947.65101
Infante, Juan Antonio; Zuazua, Enrique
1999
Exponential decay for the semilinear wave equation with localized damping in unbounded domains. Zbl 0765.35010
Zuazua, E.
1991
Stabilization of the Korteweg-de Vries equation with localized damping. Zbl 1039.35107
Perla Menzala, G.; Vasconcellos, C. F.; Zuazua, E.
2002
Large time asymptotics for partially dissipative hyperbolic systems. Zbl 1237.35017
Beauchard, Karine; Zuazua, Enrique
2011
The turnpike property in finite-dimensional nonlinear optimal control. Zbl 1301.49010
Trélat, Emmanuel; Zuazua, Enrique
2015
Stabilization and control for the subcritical semilinear wave equation. Zbl 1036.35033
Dehman, Belhassen; Lebeau, Gilles; Zuazua, Enrique
2003
Long-time behavior of a coupled heat-wave system arising in fluid-structure interaction. Zbl 1178.74075
Zhang, Xu; Zuazua, Enrique
2007
The rate at which energy decays in a string damped at one end. Zbl 0847.35078
Cox, Steven; Zuazua, Enrique
1995
Decay of solutions of the system of thermoelasticity of type III. Zbl 1136.74318
Zhang, Xu; Zuazua, Enrique
2003
Asymptotic behaviour and source-type solutions for a diffusion-convection equation. Zbl 0807.35059
Escobedo, Miguel; Vazquez, Juan Luis; Zuazua, Enrike
1993
Exact controllability for the semilinear wave equation. Zbl 0638.49017
Zuazua, Enrike
1990
Stability and decay for a class of nonlinear hyperbolic problems. Zbl 0677.35069
Zuazua, Enrike
1988
Decay rates for dissipative wave equations. Zbl 0939.35126
Liu, Wei-Jiu; Zuazua, Enrique
1999
Polynomial decay for a hyperbolic-parabolic coupled system. Zbl 1077.35030
Rauch, Jeffrey; Zhang, Xu; Zuazua, Enrique
2005
Long time versus steady state optimal control. Zbl 1287.49006
Porretta, Alessio; Zuazua, Enrique
2013
Polynomial decay and control of a 1D hyperbolic-parabolic coupled system. Zbl 1064.93008
Zhang, Xu; Zuazua, Enrique
2004
Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity. Zbl 1033.65080
Tcheugoué Tébou, Louis Roder; Zuazua, Enrique
2003
Exact controllability and stabilization of a vibrating string with an interior point mass. Zbl 0853.93018
Hansen, Scott; Zuazua, Enrique
1995
Moments, Dirac deltas and expansion of functions. (Moments, masses de Dirac et décomposition de fonctions.) Zbl 0755.45019
Duoandikoetxea, Javier; Zuazua, Enrique
1992
Boundary observability for the finite-difference space semi-discretizations of the 2-D wave equation in the square. Zbl 0939.93016
Zuazua, E.
1999
Global attractors for semilinear wave equations with locally distributed nonlinear damping and critical exponent. Zbl 0815.35069
Feireisl, Eduard; Zuazua, Enrique
1993
On the equivalence of minimal time and minimal norm controls for internally controlled heat equations. Zbl 1257.49005
Wang, Gengsheng; Zuazua, Enrique
2012
Sharp observability estimates for heat equations. Zbl 1251.93040
Ervedoza, Sylvain; Zuazua, Enrique
2011
Large-time behavior for a simplified 1D model of fluid-solid interaction. Zbl 1071.74017
Vázquez, Juan Luis; Zuazua, Enrique
2003
Null controllability of a system of viscoelasticity with a moving control. Zbl 1295.35052
Chaves-Silva, Felipe W.; Rosier, Lionel; Zuazua, Enrique
2014
Local elliptic regularity for the Dirichlet fractional Laplacian. Zbl 1360.35033
Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
2017
Controllability of partial differential equations and its semi-discrete approximations. Zbl 1005.35019
Zuazua, Enrique
2002
Stabilization of the wave equation on 1-d networks. Zbl 1203.93184
Valein, Julie; Zuazua, Enrique
2009
Numerical approximation of null controls for the heat equation: ill-posedness and remedies. Zbl 1203.35015
Münch, Arnaud; Zuazua, Enrique
2010
A diffusion-convection equation in several space dimensions. Zbl 0791.35059
Escobedo, Miguel; Vázquez, Juan Luis; Zuazua, Enrike
1993
Finite dimensional null controllability for the semilinear heat equation. Zbl 0872.93014
Zuazua, Enrique
1997
Null controllability for the heat equation with singular inverse-square potentials. Zbl 1145.93009
Vancostenoble, J.; Zuazua, E.
2008
Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations. Zbl 1079.35017
López, Antonio; Zhang, Xu; Zuazua, Enrique
2000
On the lack of null-controllability of the heat equation on the half-line. Zbl 0969.35022
Micu, Sorin; Zuazua, Enrique
2001
Uniform boundary controllability of a discrete 1-D wave equation. Zbl 1157.93324
Negreanu, Mihaela; Zuazua, Enrique
2003
Optimal shape and location of sensors for parabolic equations with random initial data. Zbl 1319.35272
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2015
Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Zbl 0959.93025
Zuazua, Enrique
1999
Stabilization of the Schrödinger equation. Zbl 0814.35008
Machtyngier, E.; Zuazua, E.
1994
Uniform boundary stabilization of the finite difference space discretization of the 1-D wave equation. Zbl 1119.65086
Tebou, Louis T.; Zuazua, Enrique
2007
A systematic method for building smooth controls for smooth data. Zbl 1219.93011
Ervedoza, Sylvain; Zuazua, Enrique
2010
On the controllability of fractional order parabolic equation. Zbl 1116.93022
Micu, Sorin; Zuazua, Enrique
2006
Stability results for the wave equation with indefinite damping. Zbl 0878.35067
Freitas, Pedro; Zuazua, Enrique
1996
Uniformly exponentially stable approximations for a class of damped systems. Zbl 1163.74019
Ervedoza, Sylvain; Zuazua, Enrique
2009
Averaged control. Zbl 1309.93029
Zuazua, Enrique
2014
Contrôlabilité exacte d’un modèle de plaques vibrantes en un temps arbitrairement petit. (Exact controllability of a vibrating plate model for an arbitrarily small time). Zbl 0611.49028
Zuazua, Enrike
1987
Entropy solutions for diffusion-convection equations with partial diffusivity. Zbl 0803.35084
Escobedo, M.; Vazquez, J. L.; Zuazua, Enrike
1994
On the null controllability of the one-dimensional heat equation with BV coefficients. Zbl 1119.93311
Fernández-Cara, Enrique; Zuazua, Enrique
2002
Numerical approximation of exact controls for waves. Zbl 1282.93001
Ervedoza, Sylvain; Zuazua, Enrique
2013
Concentration and lack of observability of waves in highly heterogeneous media. Zbl 1016.35003
Castro, C.; Zuazua, E.
2002
Control and numerical approximation of the wave and heat equations. Zbl 1108.93023
Zuazua, Enrique
2006
Optimal location of controllers for the one-dimensional wave equation. Zbl 1296.49004
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2013
Controllability of evolution equations with memory. Zbl 1368.93032
Chaves-Silva, Felipe W.; Zhang, Xu; Zuazua, Enrique
2017
Switching control. Zbl 1203.49011
Zuazua, Enrique
2011
On the lack of observability for wave equations: a Gaussian beam approach. Zbl 1024.35062
Macià, Fabricio; Zuazua, Enrique
2002
Optimal observation of the one-dimensional wave equation. Zbl 1302.93052
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2013
Complexity of large time behaviour of evolution equations with bounded data. Zbl 1002.35020
Vázquez, J. L.; Zuazua, E.
2002
Some controllability results for the 2D Kolmogorov equation. Zbl 1172.93005
Beauchard, K.; Zuazua, E.
2009
Averaged control and observation of parameter-depending wave equations. (Contrôle et observation en moyenne d’équations des ondes dépendant de paramètres.) Zbl 1302.35043
Lazar, Martin; Zuazua, Enrique
2014
Singular internal stabilization of the wave equation. Zbl 0920.35029
Jaffard, Stéphane; Tucsnak, Marius; Zuazua, Enrique
1998
Lack of collision in a simplified 1D model for fluid-solid interaction. Zbl 1387.35634
Vázquez, Juan Luis; Zuazua, Enrique
2006
Spike controls for elliptic and parabolic PDEs. Zbl 1267.49005
Casas, E.; Zuazua, E.
2013
An alternating descent method for the optimal control of the inviscid Burgers equation in the presence of shocks. Zbl 1160.35012
Castro, Carlos; Palacios, Francisco; Zuazua, Enrique
2008
Controllability of the linear system of thermoelasticity. Zbl 0846.93008
Zuazua, Enrique
1995
Boundary controllability of a hybrid system consisting in two flexible beams connected by a point mass. Zbl 0909.35085
Castro, Carlos; Zuazua, Enrique
1998
Numerical dispersive schemes for the nonlinear Schrödinger equation. Zbl 1192.65127
Ignat, Liviu I.; Zuazua, Enrique
2009
Sparse initial data identification for parabolic PDE and its finite element approximations. Zbl 1327.35131
Casas, Eduardo; Vexler, Boris; Zuazua, Enrique
2015
Identification of the class of initial data for the insensitizing control of the heat equation. Zbl 1152.35387
De Teresa, Luz; Zuazua, Enrique
2009
On the lack of null-controllability of the heat equation on the half space. Zbl 0991.35010
Micu, S.; Zuazua, E.
2001
Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms. Zbl 0997.93048
Cabanillas, V. R.; De Menezes, S. B.; Zuazua, E.
2001
Hardy inequalities, observability, and control for the wave and Schrödinger equations with singular potentials. Zbl 1200.35008
Vancostenoble, J.; Zuazua, E.
2009
Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Zbl 1335.49012
Gugat, Martin; Trélat, Emmanuel; Zuazua, Enrique
2016
Boundary controllability of the finite-difference space semi-discretizations of the beam equation. Zbl 1063.93025
León, Liliana; Zuazua, Enrique
2002
Null controllability for wave equations with memory. Zbl 1370.93051
Lü, Qi; Zhang, Xu; Zuazua, Enrique
2017
Large time behavior for convection-diffusion equations in $$\mathbb{R}^N$$ with asymptotically constant diffusion. Zbl 0931.35068
Duro, Gema; Zuazua, Enrique
1999
Boundary controllability of a linear hybrid system arising in the control of noise. Zbl 0888.35017
Micu, Sorin; Zuazua, Enrique
1997
Null controllability of linear heat and wave equations with nonlocal spatial terms. Zbl 1346.93071
Fernández-Cara, Enrique; Lü, Qi; Zuazua, Enrique
2016
Averaged controllability for random evolution Partial Differential Equations. Zbl 1332.93058
Lü, Qi; Zuazua, Enrique
2016
Asymptotic expansion for damped wave equations with periodic coefficients. Zbl 1013.35014
Orive, R.; Zuazua, E.; Pazoto, A. F.
2001
Convergence of a multigrid method for the controllability of a 1-D wave equation. Zbl 1038.65054
Negreanu, Mihaela; Zuazua, Enrique
2004
On the observability of time-discrete conservative linear systems. Zbl 1143.65044
Ervedoza, Sylvain; Zheng, Chuang; Zuazua, Enrique
2008
Controllability of star-shaped networks of strings. Zbl 0986.35018
Dáger, René; Zuazua, Enrique
2001
Unique continuation and control for the heat equation from an oscillating lower dimensional manifold. Zbl 1101.93010
Castro, Carlos; Zuazua, Enrique
2005
Turnpike in Lipschitz-nonlinear optimal control. Zbl 1484.49006
Esteve-Yagüe, Carlos; Geshkovski, Borjan; Pighin, Dario; Zuazua, Enrique
2022
Model predictive control with random batch methods for a guiding problem. Zbl 1476.49038
Ko, Dongnam; Zuazua, Enrique
2021
Averaged dynamics and control for heat equations with random diffusion. Zbl 1480.93191
Bárcena-Petisco, Jon Asier; Zuazua, Enrique
2021
Classical system theory revisited for turnpike in standard state space systems and impulse controllable descriptor systems. Zbl 1475.49040
Heiland, Jan; Zuazua, Enrique
2021
Nonnegative control of finite-dimensional linear systems. Zbl 1466.93020
Lohéac, Jérôme; Trélat, Emmanuel; Zuazua, Enrique
2021
Controllability of one-dimensional viscous free boundary flows. Zbl 1467.93034
Geshkovski, Borjan; Zuazua, Enrique
2021
Controllability of the one-dimensional fractional heat equation under positivity constraints. Zbl 1446.93012
Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
2020
Shape turnpike for linear parabolic PDE models. Zbl 1451.93170
Lance, Gontran; Trélat, Emmanuel; Zuazua, Enrique
2020
Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. Zbl 1451.93033
Ruiz-Balet, Domènec; Zuazua, Enrique
2020
Asymptotic behavior and control of a “Guidance by repulsion” model. Zbl 1451.93306
Ko, Dongnam; Zuazua, Enrique
2020
Controllability of shadow reaction-diffusion systems. Zbl 1477.35292
Hernández-Santamaría, Víctor; Zuazua, Enrique
2020
The inverse problem for Hamilton-Jacobi equations and semiconcave envelopes. Zbl 1453.35189
Esteve, Carlos; Zuazua, Enrique
2020
Full probabilistic solution of a finite dimensional linear control system with random initial and final conditions. Zbl 1447.93338
Cortés, J.-C.; Navarro-Quiles, A.; Romero, J.-V.; Roselló, M.-D.; Zuazua, Enrique
2020
Propagation of one- and two-dimensional discrete waves under finite difference approximation. Zbl 1457.35009
Biccari, Umberto; Marica, Aurora; Zuazua, Enrique
2020
Controllability and positivity constraints in population dynamics with age structuring and diffusion. Zbl 1422.93017
Maity, Debayan; Tucsnak, Marius; Zuazua, Enrique
2019
Internal observability for coupled systems of linear partial differential equations. Zbl 1409.35059
Lissy, Pierre; Zuazua, Enrique
2019
Greedy optimal control for elliptic problems and its application to turnpike problems. Zbl 1408.49018
Hernández-Santamaría, Víctor; Lazar, Martin; Zuazua, Enrique
2019
Controllability under positivity constraints of multi-d wave equations. Zbl 1428.35202
Pighin, Dario; Zuazua, Enrique
2019
Dynamics and control for multi-agent networked systems: a finite-difference approach. Zbl 1428.93017
Biccari, Umberto; Ko, Dongnam; Zuazua, Enrique
2019
Phase portrait control for 1D monostable and bistable reaction-diffusion equations. Zbl 1406.35161
Pouchol, Camille; Trélat, Emmanuel; Zuazua, Enrique
2019
A two-dimensional “flea on the elephant” phenomenon and its numerical visualization. Zbl 1408.35110
Bianchini, Roberta; Gosse, Laurent; Zuazua, Enrique
2019
Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions. Zbl 1410.35090
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2019
A parabolic approach to the control of opinion spreading. Zbl 1447.91120
Ruiz-Balet, Domènec; Zuazua, Enrique
2019
Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids. Zbl 1438.35258
Morales-Hernández, M.; Zuazua, E.
2019
Controllability of a class of infinite dimensional systems with age structure. Zbl 1446.93014
Maity, Debayan; Tucsnak, Marius; Zuazua, Enrique
2019
Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces. Zbl 1387.49042
Trélat, Emmanuel; Zhang, Can; Zuazua, Enrique
2018
Controllability under positivity constraints of semilinear heat equations. Zbl 1416.35142
Pighin, Dario; Zuazua, Enrique
2018
Local regularity for fractional heat equations. Zbl 1415.35072
Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
2018
Minimal controllability time for finite-dimensional control systems under state constraints. Zbl 1406.93059
Lohéac, Jérôme; Trélat, Emmanuel; Zuazua, Enrique
2018
Internal controllability for parabolic systems involving analytic non-local terms. Zbl 1391.35187
Lissy, Pierre; Zuazua, Enrique
2018
Allee optimal control of a system in ecology. Zbl 1411.93198
Trélat, Emmanuel; Zhu, Jiamin; Zuazua, Enrique
2018
Optimal shape design for 2D heat equations in large time. Zbl 1474.35351
Trélat, Emmanuel; Zhang, Can; Zuazua, Enrique
2018
Local elliptic regularity for the Dirichlet fractional Laplacian. Zbl 1360.35033
Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
2017
Controllability of evolution equations with memory. Zbl 1368.93032
Chaves-Silva, Felipe W.; Zhang, Xu; Zuazua, Enrique
2017
Null controllability for wave equations with memory. Zbl 1370.93051
Lü, Qi; Zhang, Xu; Zuazua, Enrique
2017
Minimal controllability time for the heat equation under unilateral state or control constraints. Zbl 1370.35156
Lohéac, Jérôme; Trélat, Emmanuel; Zuazua, Enrique
2017
Averaged controllability of parameter dependent conservative semigroups. Zbl 1352.93025
Lohéac, Jérôme; Zuazua, Enrique
2017
Numerical hypocoercivity for the Kolmogorov equation. Zbl 1351.65059
Porretta, Alessio; Zuazua, Enrique
2017
Addendum to: “Local elliptic regularity for the Dirichlet fractional Laplacian”. Zbl 06791441
Biccari, Umberto; Warma, Mahamadi; Zuazua, Enrique
2017
Actuator design for parabolic distributed parameter systems with the moment method. Zbl 1361.49020
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2017
Filtered gradient algorithms for inverse design problems of one-dimensional Burgers equation. Zbl 1375.35630
Gosse, Laurent; Zuazua, Enrique
2017
Decay rates for elastic-thermoelastic star-shaped networks. Zbl 1377.35022
Han, Zhong-Jie; Zuazua, Enrique
2017
Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Zbl 1335.49012
Gugat, Martin; Trélat, Emmanuel; Zuazua, Enrique
2016
Null controllability of linear heat and wave equations with nonlocal spatial terms. Zbl 1346.93071
Fernández-Cara, Enrique; Lü, Qi; Zuazua, Enrique
2016
Averaged controllability for random evolution Partial Differential Equations. Zbl 1332.93058
Lü, Qi; Zuazua, Enrique
2016
Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis. Zbl 1433.65157
Ervedoza, Sylvain; Marica, Aurora; Zuazua, Enrique
2016
Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains. Zbl 1338.35320
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2016
Remarks on long time versus steady state optimal control. Zbl 1369.49008
Porretta, Alessio; Zuazua, Enrique
2016
On the lack of controllability of fractional in time ODE and PDE. Zbl 1342.93027
Lü, Qi; Zuazua, Enrique
2016
Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function. Zbl 1341.35085
Biccari, Umberto; Zuazua, Enrique
2016
From averaged to simultaneous controllability. Zbl 1348.93052
Lohéac, Jérôme; Zuazua, Enrique
2016
Numerical aspects of large-time optimal control of Burgers equation. Zbl 1350.49036
Allahverdi, Navid; Pozo, Alejandro; Zuazua, Enrique
2016
Greedy controllability of finite dimensional linear systems. Zbl 1348.93051
Lazar, Martin; Zuazua, Enrique
2016
Stable observation of additive superpositions of partial differential equations. Zbl 1336.93036
Zuazua, Enrique
2016
Exact penalization of terminal constraints for optimal control problems. Zbl 1353.49005
Gugat, Martin; Zuazua, Enrique
2016
Decay rates for $$1-d$$ heat-wave planar networks. Zbl 1355.35023
Han, Zhong-Jie; Zuazua, Enrique
2016
Control of 2D scalar conservation laws in the presence of shocks. Zbl 1336.35239
Lecaros, Rodrigo; Zuazua, Enrique
2016
Optimal strategies for driving a mobile agent in a “guidance by repulsion” model. Zbl 07249750
Escobedo, R.; Ibañez, A.; Zuazua, E.
2016
Numerical aspects of sonic-boom minimization. Zbl 1345.49039
Allahverdi, Navid; Pozo, Alejandro; Zuazua, Enrique
2016
Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems. (Dépendance Lipschitz des coefficients comme fonction de la résolvante et approximation greedy pour les problèmes elliptiques scalaires.) Zbl 1349.35426
2016
The turnpike property in finite-dimensional nonlinear optimal control. Zbl 1301.49010
Trélat, Emmanuel; Zuazua, Enrique
2015
Optimal shape and location of sensors for parabolic equations with random initial data. Zbl 1319.35272
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2015
Sparse initial data identification for parabolic PDE and its finite element approximations. Zbl 1327.35131
Casas, Eduardo; Vexler, Boris; Zuazua, Enrique
2015
Complexity and regularity of maximal energy domains for the wave equation with fixed initial data. Zbl 1332.93069
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2015
Generation of 2D water waves by moving bottom disturbances. Zbl 1330.35338
Nersisyan, Hayk; Dutykh, Denys; Zuazua, Enrique
2015
Weak observability estimates for 1-D wave equations with rough coefficients. Zbl 1320.93027
Fanelli, Francesco; Zuazua, Enrique
2015
Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws. Zbl 1320.65117
Ignat, Liviu I.; Pozo, Alejandro; Zuazua, Enrique
2015
Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach. Zbl 1375.81163
Marica, Aurora; Zuazua, Enrique
2015
Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces. Zbl 1311.65112
Lescarret, Vincent; Zuazua, Enrique
2015
Transmutation techniques and observability for time-discrete approximation schemes of conservative systems. Zbl 1320.65097
Ervedoza, Sylvain; Zuazua, Enrique
2015
Null controllability of a system of viscoelasticity with a moving control. Zbl 1295.35052
Chaves-Silva, Felipe W.; Rosier, Lionel; Zuazua, Enrique
2014
Averaged control. Zbl 1309.93029
Zuazua, Enrique
2014
Averaged control and observation of parameter-depending wave equations. (Contrôle et observation en moyenne d’équations des ondes dépendant de paramètres.) Zbl 1302.35043
Lazar, Martin; Zuazua, Enrique
2014
Robust null controllability for heat equations with unknown switching control mode. Zbl 1301.93028
Lü, Qi; Zuazua, Enrique
2014
Tracking control of 1D scalar conservation laws in the presence of shocks. Zbl 1325.49032
Lecaros, Rodrigo; Zuazua, Enrique
2014
Recovery of an initial temperature from discrete sampling. Zbl 1298.35250
DeVore, Ronald; Zuazua, Enrique
2014
Symmetric discontinuous Galerkin methods for 1-D waves. Fourier analysis, propagation, observability and applications. Zbl 1295.65097
Marica, Aurora; Zuazua, Enrique
2014
Boundary stabilization of numerical approximations of the 1-D variable coefficients wave equation: A numerical viscosity approach. Zbl 1322.65091
Marica, Aurora; Zuazua, Enrique
2014
Long time versus steady state optimal control. Zbl 1287.49006
Porretta, Alessio; Zuazua, Enrique
2013
Numerical approximation of exact controls for waves. Zbl 1282.93001
Ervedoza, Sylvain; Zuazua, Enrique
2013
Optimal location of controllers for the one-dimensional wave equation. Zbl 1296.49004
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2013
Optimal observation of the one-dimensional wave equation. Zbl 1302.93052
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
2013
Spike controls for elliptic and parabolic PDEs. Zbl 1267.49005
Casas, E.; Zuazua, E.
2013
Improved multipolar Hardy inequalities. Zbl 1283.35098
Cazacu, Cristian; Zuazua, Enrique
2013
On the quadratic finite element approximation of 1D waves: propagation, observation, control, and numerical implementation. Zbl 1273.65146
Marica, Aurora; Zuazua, Enrique
2013
Asymptotic expansions for anisotropic heat kernels. Zbl 1263.35208
Ignat, Liviu I.; Zuazua, Enrique
2013
Sensitivity analysis of $$1-d$$ steady forced scalar conservation laws. Zbl 1263.35024
Ersoy, Mehmet; Feireisl, Eduard; Zuazua, Enrique
2013
Blowup for a time-oscillating nonlinear heat equation. Zbl 1324.35099
Cazenave, Th.; Escobedo, M.; Zuazua, E.
2013
On the equivalence of minimal time and minimal norm controls for internally controlled heat equations. Zbl 1257.49005
Wang, Gengsheng; Zuazua, Enrique
2012
Null controllability of viscous Hamilton-Jacobi equations. Zbl 1244.93027
Porretta, Alessio; Zuazua, Enrique
2012
Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations. Zbl 1256.65085
Ignat, Liviu I.; Zuazua, Enrique
2012
A remark on the observability of conservative linear systems. Zbl 1394.35267
Zuazua, Enrique
2012
On the quadratic finite element approximation of one-dimensional waves: propagation, observation, and control. Zbl 1319.65090
Marica, Aurora; Zuazua, Enrique
2012
Approximating travelling waves by equilibria of non-local equations. Zbl 1248.35038
Arrieta, Jose M.; López-Fernández, María; Zuazua, Enrique
2012
Large time asymptotics for partially dissipative hyperbolic systems. Zbl 1237.35017
Beauchard, Karine; Zuazua, Enrique
2011
Sharp observability estimates for heat equations. Zbl 1251.93040
Ervedoza, Sylvain; Zuazua, Enrique
2011
Switching control. Zbl 1203.49011
Zuazua, Enrique
2011
Observability of heat processes by transmutation without geometric restrictions. Zbl 1244.35028
Ervedoza, Sylvain; Zuazua, Enrique
2011
The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide. Zbl 1213.35107
Krejčiřík, David; Zuazua, Enrique
2011
Flux identification for 1-d scalar conservation laws in the presence of shocks. Zbl 1228.49004
Castro, Carlos; Zuazua, Enrique
2011
...and 220 more Documents
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### Cited by 2,823 Authors

 146 Zuazua, Enrique 41 Cavalcanti, Marcelo Moreira 41 Fernández-Cara, Enrique 35 Xu, Gen-Qi 33 Messaoudi, Salim A. 32 Nicaise, Serge 30 Ammari, Kais 29 Domingos Cavalcanti, Valéria Neves 29 Trélat, Emmanuel 27 Guo, Bao-Zhu 26 Münch, Arnaud 25 Ervedoza, Sylvain 25 Micu, Sorin 25 Tcheugoué Tébou, Louis Roder 25 Tucsnak, Marius 24 Mustafa, Muhammad Islam 23 Kunisch, Karl 23 Pazoto, Ademir Fernando 21 Lasiecka, Irena 20 Wang, Gengsheng 20 Zhang, Xu 19 Coron, Jean-Michel 19 Gugat, Martin 19 Han, Zhongjie 19 Maniar, Lahcen 19 Rao, Bopeng 19 Takahashi, Takéo 18 Alabau-Boussouira, Fatiha 18 Leugering, Günter 18 Li, Tatsien 17 González-Burgos, Manuel 17 Ignat, Liviu I. 17 Limaco, Juan 17 Wang, Junmin 17 Warma, Mahamadi 16 Avdonin, Sergeĭ Anatol’evich 16 Cannarsa, Piermarco 16 de Teresa, Luz 16 Le Rousseau, Jérôme H. 16 Lü, Qi 16 Martinez, Patrick 16 Nakao, Mitsuhiro 16 Privat, Yannick 15 Araruna, Fágner Dias 15 Kaikina, Elena Igorevna 15 Komornik, Vilmos 15 Vancostenoble, Judith 14 Beauchard, Karine 14 Guerrero, Sergio 14 Krejčiřík, David 14 Liu, Xu 14 Muñoz Rivera, Jaime Edilberto 14 Said-Houari, Belkacem 13 Benabdallah, Assia 13 Gao, Hang 13 Grüne, Lars 13 Hernández-Santamaría, Víctor 13 Lissy, Pierre 13 Liu, Wenjun 13 Rosier, Lionel 13 Wang, Lijuan 12 Biccari, Umberto 12 Fu, Xiaoyu 12 Laurent, Camille 12 Léautaud, Matthieu 12 Park, Jong Yeoul 12 Periago, Francisco 12 Porretta, Alessio 11 Aouadi, Moncef 11 Chaves-Silva, Felipe Wallison 11 Clark, Haroldo Rodrigues 11 Haraux, Alain 11 Krstić, Miroslav 11 Laurençot, Philippe 11 Loreti, Paola 11 Mitra, Debanjana 11 Phung, Kim Dang 10 Ammar-Khodja, Farid 10 Balachandran, Krishnan 10 Boyer, Franck 10 Cîndea, Nicolae 10 De Menezes, Silvano Bezerra 10 Escobedo Martínez, Miguel 10 Filippas, Stathis 10 Naumkin, Pavel Ivanovich 10 Ortega, Jaime H. 10 Osses, Axel 10 Pignotti, Cristina 10 Puel, Jean-Pierre 10 Quintanilla de Latorre, Ramón 10 Roventa, Ionel 10 Tertikas, Achilles 10 Wang, Liangwei 10 Wehbe, Ali 10 Yao, Pengfei 9 Berrahmoune, Larbi 9 Cerpa, Eduardo 9 Corrêa, Wellington José 9 Du, Runmei 9 Fragnelli, Genni ...and 2,723 more Authors
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### Cited in 365 Serials

 198 Journal of Mathematical Analysis and Applications 183 Journal of Differential Equations 167 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 107 SIAM Journal on Control and Optimization 99 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 83 Systems & Control Letters 81 Journal de Mathématiques Pures et Appliquées. Neuvième Série 75 Comptes Rendus. Mathématique. Académie des Sciences, Paris 68 Mathematical Control and Related Fields 50 Journal of Functional Analysis 49 Applicable Analysis 49 Mathematical Methods in the Applied Sciences 45 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 45 Evolution Equations and Control Theory 42 Applied Mathematics and Optimization 42 Journal of Optimization Theory and Applications 41 ZAMP. Zeitschrift für angewandte Mathematik und Physik 40 Journal of Evolution Equations 38 Communications in Partial Differential Equations 36 Applied Mathematics Letters 33 Automatica 33 MCSS. Mathematics of Control, Signals, and Systems 31 Discrete and Continuous Dynamical Systems 28 Journal of Mathematical Physics 28 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 28 Communications on Pure and Applied Analysis 27 Discrete and Continuous Dynamical Systems. Series B 26 Journal of Dynamical and Control Systems 25 Discrete and Continuous Dynamical Systems. Series S 24 Computers & Mathematics with Applications 24 Communications in Contemporary Mathematics 23 Applied Mathematics and Computation 22 Acta Applicandae Mathematicae 21 Archive for Rational Mechanics and Analysis 20 Nonlinear Analysis. Real World Applications 19 Numerische Mathematik 19 Transactions of the American Mathematical Society 19 Chinese Annals of Mathematics. Series B 18 International Journal of Control 18 SIAM Journal on Mathematical Analysis 16 Abstract and Applied Analysis 16 Boundary Value Problems 15 Calculus of Variations and Partial Differential Equations 14 NoDEA. Nonlinear Differential Equations and Applications 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Mathematics of Computation 13 Computational Optimization and Applications 13 Journal of the European Mathematical Society (JEMS) 13 Journal of Systems Science and Complexity 13 Advances in Difference Equations 12 European Journal of Control 12 Journal of Hyperbolic Differential Equations 12 Nonlinear Analysis. Theory, Methods & Applications 11 Journal of the Franklin Institute 11 Asymptotic Analysis 10 Journal d’Analyse Mathématique 10 Integral Equations and Operator Theory 10 Journal of Computational and Applied Mathematics 10 Quarterly of Applied Mathematics 10 Mathematical and Computer Modelling 10 Journal of Dynamics and Differential Equations 10 Mathematical Problems in Engineering 10 Vietnam Journal of Mathematics 10 Acta Mathematica Sinica. English Series 10 Portugaliae Mathematica. Nova Série 10 Mediterranean Journal of Mathematics 10 Networks and Heterogeneous Media 9 Mathematische Annalen 9 Proceedings of the American Mathematical Society 9 Acta Mathematicae Applicatae Sinica. English Series 9 Advances in Computational Mathematics 9 Differential Equations 9 Advances in Nonlinear Analysis 8 Applied Numerical Mathematics 8 Journal of Mathematical Sciences (New York) 8 Computational and Applied Mathematics 8 Inverse Problems in Science and Engineering 7 Communications in Mathematical Physics 7 Journal of Computational Physics 7 Nonlinearity 7 Journal of Scientific Computing 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 SIAM Journal on Applied Mathematics 7 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 7 Journal of Inequalities and Applications 7 Séminaire Laurent Schwartz. EDP et Applications 6 Inverse Problems 6 Journal of Statistical Physics 6 Numerical Functional Analysis and Optimization 6 SIAM Journal on Numerical Analysis 6 Applications of Mathematics 6 Journal of Inverse and Ill-Posed Problems 6 Journal of Applied Mathematics 6 Journal of Applied Mathematics and Computing 5 Rocky Mountain Journal of Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Calcolo 5 Mathematische Nachrichten 5 Optimization 5 European Journal of Applied Mathematics ...and 265 more Serials
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### Cited in 50 Fields

 2,445 Partial differential equations (35-XX) 1,371 Systems theory; control (93-XX) 468 Mechanics of deformable solids (74-XX) 367 Calculus of variations and optimal control; optimization (49-XX) 290 Numerical analysis (65-XX) 209 Operator theory (47-XX) 192 Fluid mechanics (76-XX) 134 Ordinary differential equations (34-XX) 111 Real functions (26-XX) 81 Dynamical systems and ergodic theory (37-XX) 76 Functional analysis (46-XX) 64 Probability theory and stochastic processes (60-XX) 62 Biology and other natural sciences (92-XX) 55 Integral equations (45-XX) 43 Global analysis, analysis on manifolds (58-XX) 43 Operations research, mathematical programming (90-XX) 39 Statistical mechanics, structure of matter (82-XX) 37 Quantum theory (81-XX) 32 Classical thermodynamics, heat transfer (80-XX) 31 Optics, electromagnetic theory (78-XX) 31 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 30 Harmonic analysis on Euclidean spaces (42-XX) 27 Mechanics of particles and systems (70-XX) 16 Differential geometry (53-XX) 12 Difference and functional equations (39-XX) 10 Functions of a complex variable (30-XX) 9 Potential theory (31-XX) 9 Special functions (33-XX) 8 Geophysics (86-XX) 6 Combinatorics (05-XX) 6 Topological groups, Lie groups (22-XX) 6 Approximations and expansions (41-XX) 6 Computer science (68-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Abstract harmonic analysis (43-XX) 4 Integral transforms, operational calculus (44-XX) 4 Information and communication theory, circuits (94-XX) 3 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 General topology (54-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Astronomy and astrophysics (85-XX)

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