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## Coulombel, Jean-François

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 Author ID: coulombel.jean-francois Published as: Coulombel, Jean-François; Coulombel, Jean-Francois; Coulombel, J.-F.; Coulombel, Jean Francois
 Documents Indexed: 56 Publications since 2002, including 3 Books
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#### Co-Authors

 16 single-authored 8 Goudon, Thierry 8 Williams, Mark 7 Secchi, Paolo 6 Benzoni-Gavage, Sylvie 4 Guès, Olivier 3 Lin, Chunjin 2 Morando, Alessandro 2 Tzvetkov, Nikolay 1 Bellier-Millès, Joan 1 Berthon, Christophe 1 Besse, Christophe 1 Boutin, Benjamin 1 Buet, Christophe 1 Calgaro, Caterina 1 Chalons, Christophe 1 Després, Bruno 1 Gloria, Antoine 1 Golse, François 1 Lafitte, Pauline 1 Lagoutière, Frédéric 1 Morel, Jim E. 1 Noble, Pascal 1 Pierre, Olivier 1 Serre, Denis 1 Trebeschi, Paola 1 Turpault, Rodolphe
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#### Serials

 2 Indiana University Mathematics Journal 2 Asymptotic Analysis 2 Journal of Hyperbolic Differential Equations 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Mathematics of Computation 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Annali dell’Università di Ferrara. Nuova Serie. Sezione VII 1 Bulletin de la Société Mathématique de France 1 Calcolo 1 Gazette des Mathématiciens 1 Journal of Differential Equations 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 NoDEA. Nonlinear Differential Equations and Applications 1 Interfaces and Free Boundaries 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Panoramas et Synthèses 1 Communications in Computational Physics 1 Kinetic and Related Models 1 Analysis & PDE 1 Numerical Mathematics: Theory, Methods and Applications 1 Confluentes Mathematici 1 Matapli 1 Journal de l’École Polytechnique – Mathématiques 1 Séminaire Laurent Schwartz. EDP et Applications 1 Advances in Mathematical Fluid Mechanics
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#### Fields

 48 Partial differential equations (35-XX) 23 Fluid mechanics (76-XX) 14 Numerical analysis (65-XX) 8 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Mechanics of deformable solids (74-XX) 2 Astronomy and astrophysics (85-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Operator theory (47-XX)

#### Citations contained in zbMATH Open

43 Publications have been cited 408 times in 243 Documents Cited by Year
Nonlinear compressible vortex sheets in two space dimensions. Zbl 1160.35061
Coulombel, Jean-François; Secchi, Paolo
2008
The stability of compressible vortex sheets in two space dimensions. Zbl 1068.35100
Coulombel, Jean-François; Secchi, Paolo
2004
Shock profiles for non-equilibrium radiating gases. Zbl 1096.35086
Lin, Chunjin; Coulombel, Jean-François; Goudon, Thierry
2006
The strong relaxation limit of the multidimensional isothermal Euler equations. Zbl 1170.35477
Coulombel, Jean-François; Goudon, Thierry
2007
Relaxation approximation of the Euler equations. Zbl 1153.35002
Chalons, Christophe; Coulombel, Jean-François
2008
Diffusion approximation and entropy-based moment closure for kinetic equations. Zbl 1091.35038
Coulombel, Jean-François; Golse, François; Goudon, Thierry
2005
A priori estimates for 3D incompressible current-vortex sheets. Zbl 1250.35190
Coulombel, J.-F.; Morando, A.; Secchi, P.; Trebeschi, P.
2012
Well-posedness of hyperbolic initial boundary value problems. Zbl 1078.35066
Coulombel, Jean-François
2005
Weakly stable multidimensional shocks. Zbl 1072.35120
Coulombel, Jean-François
2004
Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems. Zbl 1218.35137
Coulombel, Jean-François; Guès, Olivier
2010
Asymptotic stability of shock profiles in radiative hydrodynamics. Zbl 1387.35497
Lin, Chunjin; Coulombel, Jean-François; Goudon, Thierry
2007
The strong relaxation limit of the multidimensional Euler equations. Zbl 1268.35099
Lin, Chunjin; Coulombel, Jean-François
2013
On the transition to instability for compressible vortex sheets. Zbl 1083.35108
Coulombel, Jean-François; Secchi, Paolo
2004
Weak stability of nonuniformly stable multidimensional shocks. Zbl 1029.35171
Coulombel, Jean-François
2002
Uniqueness of 2-D compressible vortex sheets. Zbl 1160.76040
Coulombel, Jean-François; Secchi, Paolo
2009
Stability of multidimensional undercompressive shock waves. Zbl 1039.76029
Coulombel, Jean-François
2003
Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. Zbl 1308.65142
Coulombel, Jean-François; Gloria, Antoine
2011
On the amplitude equations for weakly nonlinear surface waves. Zbl 1427.76037
Benzoni-Gavage, Sylvie; Coulombel, Jean-François
2012
Stability of finite difference schemes for hyperbolic initial boundary value problems. II. Zbl 1225.65089
Coulombel, Jean-François
2011
Stability of finite difference schemes for hyperbolic initial boundary value problems. Zbl 1205.65245
Coulombel, Jean-François
2009
Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems. Zbl 1241.35131
Coulombel, Jean-Francois; Gues, Olivier; Williams, Mark
2011
Semilinear geometric optics with boundary amplification. Zbl 1330.35242
Coulombel, Jean-Francois; Guès, Olivier; Williams, Mark
2014
The Mach stem equation and amplification in strongly nonlinear geometric optics. Zbl 1383.35221
Coulombel, Jean-François; Williams, Mark
2017
Ill-posedness of nonlocal Burgers equations. Zbl 1228.35174
Benzoni-Gavage, Sylvie; Coulombel, Jean-François; Tzvetkov, Nikolay
2011
Stability of contact discontinuities for the nonisenitropic Euler equations. Zbl 1144.35456
Coulombel, Jean-François; Morando, Alessandro
2004
Mathematical models and numerical methods for radiative transfer. Collection of papers from the summer school, Nice, France, July 31 to August 4, 2007. Zbl 1188.85001
Berthon, C. (ed.); Buet, C. (ed.); Coulombel, J.-F. (ed.); Desprès, B (ed.); Dubois, J. (ed.); Goudon, T. (ed.); Morel, J. E. (ed.); Turpault, R. (ed.)
2009
From gas dynamics to pressureless gas dynamics. Zbl 1087.35059
Coulombel, Jean-François
2006
Entropy-based moment closure for kinetic equations: Riemann problem and invariant regions. Zbl 1121.35075
Coulombel, Jean-François; Goudon, Thierry
2006
Note on a paper by Robinet, Gressier, Casalis and Moschetta. Zbl 1152.76394
Coulombel, Jean-François; Benzoni-Gavage, Sylvie; Serre, Denis
2002
The Leray-Gårding method for finite difference schemes. (La méthode de Leray et Gårding pour les schémas aux différences finies.) Zbl 1328.65175
Coulombel, Jean-François
2015
Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers. Zbl 1399.65203
Boutin, Benjamin; Coulombel, Jean Francois
2017
Singular pseudodifferential calculus for wavetrains and pulses. (Calcul pseudodifférentiel singulier pour les trains d’ondes et les pulses.) Zbl 1323.35235
Coulombel, Jean-Francois; Guès, Olivier; Williams, Mark
2014
The hyperbolic region for hyperbolic boundary value problems. Zbl 1237.35106
Coulombel, Jean-François
2011
Stability of compressible vortex sheets. Zbl 1102.76062
Coulombel, J.-F.; Secchi, P.
2005
Amplitude equations for weakly nonlinear surface waves in variational problems. Zbl 1366.76012
Benzoni-Gavage, Sylvie; Coulombel, Jean-François
2017
Nonlinear geometric optics for reflecting uniformly stable pulses. Zbl 1295.35310
Coulombel, Jean-Francois; Williams, Mark
2013
Fully discrete hyperbolic initial boundary value problems with nonzero initial data. Zbl 1355.65116
Coulombel, Jean-François
2015
Transparent numerical boundary conditions for evolution equations: derivation and stability analysis. Zbl 1422.65149
Coulombel, Jean-François
2019
Amplification of pulses in nonlinear geometric optics. Zbl 1330.35243
Coulombel, Jean-François; Williams, Mark
2014
On the strong stability of finite difference schemes for hyperbolic systems in two space dimensions. Zbl 1311.65115
Coulombel, Jean-François
2014
The Neumann numerical boundary condition for transport equations. Zbl 1437.65093
Coulombel, Jean-François; Lagoutière, Frédéric
2020
Weak stability of multidimensional shocks. Zbl 1098.35105
Coulombel, Jean-François
2003
Nonlinear stability of compressible vortex sheets. Zbl 1167.35552
Coulombel, J.-F.; Secchi, P.
2008
The Neumann numerical boundary condition for transport equations. Zbl 1437.65093
Coulombel, Jean-François; Lagoutière, Frédéric
2020
Transparent numerical boundary conditions for evolution equations: derivation and stability analysis. Zbl 1422.65149
Coulombel, Jean-François
2019
The Mach stem equation and amplification in strongly nonlinear geometric optics. Zbl 1383.35221
Coulombel, Jean-François; Williams, Mark
2017
Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers. Zbl 1399.65203
Boutin, Benjamin; Coulombel, Jean Francois
2017
Amplitude equations for weakly nonlinear surface waves in variational problems. Zbl 1366.76012
Benzoni-Gavage, Sylvie; Coulombel, Jean-François
2017
The Leray-Gårding method for finite difference schemes. (La méthode de Leray et Gårding pour les schémas aux différences finies.) Zbl 1328.65175
Coulombel, Jean-François
2015
Fully discrete hyperbolic initial boundary value problems with nonzero initial data. Zbl 1355.65116
Coulombel, Jean-François
2015
Semilinear geometric optics with boundary amplification. Zbl 1330.35242
Coulombel, Jean-Francois; Guès, Olivier; Williams, Mark
2014
Singular pseudodifferential calculus for wavetrains and pulses. (Calcul pseudodifférentiel singulier pour les trains d’ondes et les pulses.) Zbl 1323.35235
Coulombel, Jean-Francois; Guès, Olivier; Williams, Mark
2014
Amplification of pulses in nonlinear geometric optics. Zbl 1330.35243
Coulombel, Jean-François; Williams, Mark
2014
On the strong stability of finite difference schemes for hyperbolic systems in two space dimensions. Zbl 1311.65115
Coulombel, Jean-François
2014
The strong relaxation limit of the multidimensional Euler equations. Zbl 1268.35099
Lin, Chunjin; Coulombel, Jean-François
2013
Nonlinear geometric optics for reflecting uniformly stable pulses. Zbl 1295.35310
Coulombel, Jean-Francois; Williams, Mark
2013
A priori estimates for 3D incompressible current-vortex sheets. Zbl 1250.35190
Coulombel, J.-F.; Morando, A.; Secchi, P.; Trebeschi, P.
2012
On the amplitude equations for weakly nonlinear surface waves. Zbl 1427.76037
Benzoni-Gavage, Sylvie; Coulombel, Jean-François
2012
Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. Zbl 1308.65142
Coulombel, Jean-François; Gloria, Antoine
2011
Stability of finite difference schemes for hyperbolic initial boundary value problems. II. Zbl 1225.65089
Coulombel, Jean-François
2011
Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems. Zbl 1241.35131
Coulombel, Jean-Francois; Gues, Olivier; Williams, Mark
2011
Ill-posedness of nonlocal Burgers equations. Zbl 1228.35174
Benzoni-Gavage, Sylvie; Coulombel, Jean-François; Tzvetkov, Nikolay
2011
The hyperbolic region for hyperbolic boundary value problems. Zbl 1237.35106
Coulombel, Jean-François
2011
Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems. Zbl 1218.35137
Coulombel, Jean-François; Guès, Olivier
2010
Uniqueness of 2-D compressible vortex sheets. Zbl 1160.76040
Coulombel, Jean-François; Secchi, Paolo
2009
Stability of finite difference schemes for hyperbolic initial boundary value problems. Zbl 1205.65245
Coulombel, Jean-François
2009
Mathematical models and numerical methods for radiative transfer. Collection of papers from the summer school, Nice, France, July 31 to August 4, 2007. Zbl 1188.85001
Berthon, C.; Buet, C.; Coulombel, J.-F.; Desprès, B; Dubois, J.; Goudon, T.; Morel, J. E.; Turpault, R.
2009
Nonlinear compressible vortex sheets in two space dimensions. Zbl 1160.35061
Coulombel, Jean-François; Secchi, Paolo
2008
Relaxation approximation of the Euler equations. Zbl 1153.35002
Chalons, Christophe; Coulombel, Jean-François
2008
Nonlinear stability of compressible vortex sheets. Zbl 1167.35552
Coulombel, J.-F.; Secchi, P.
2008
The strong relaxation limit of the multidimensional isothermal Euler equations. Zbl 1170.35477
Coulombel, Jean-François; Goudon, Thierry
2007
Asymptotic stability of shock profiles in radiative hydrodynamics. Zbl 1387.35497
Lin, Chunjin; Coulombel, Jean-François; Goudon, Thierry
2007
Shock profiles for non-equilibrium radiating gases. Zbl 1096.35086
Lin, Chunjin; Coulombel, Jean-François; Goudon, Thierry
2006
From gas dynamics to pressureless gas dynamics. Zbl 1087.35059
Coulombel, Jean-François
2006
Entropy-based moment closure for kinetic equations: Riemann problem and invariant regions. Zbl 1121.35075
Coulombel, Jean-François; Goudon, Thierry
2006
Diffusion approximation and entropy-based moment closure for kinetic equations. Zbl 1091.35038
Coulombel, Jean-François; Golse, François; Goudon, Thierry
2005
Well-posedness of hyperbolic initial boundary value problems. Zbl 1078.35066
Coulombel, Jean-François
2005
Stability of compressible vortex sheets. Zbl 1102.76062
Coulombel, J.-F.; Secchi, P.
2005
The stability of compressible vortex sheets in two space dimensions. Zbl 1068.35100
Coulombel, Jean-François; Secchi, Paolo
2004
Weakly stable multidimensional shocks. Zbl 1072.35120
Coulombel, Jean-François
2004
On the transition to instability for compressible vortex sheets. Zbl 1083.35108
Coulombel, Jean-François; Secchi, Paolo
2004
Stability of contact discontinuities for the nonisenitropic Euler equations. Zbl 1144.35456
Coulombel, Jean-François; Morando, Alessandro
2004
Stability of multidimensional undercompressive shock waves. Zbl 1039.76029
Coulombel, Jean-François
2003
Weak stability of multidimensional shocks. Zbl 1098.35105
Coulombel, Jean-François
2003
Weak stability of nonuniformly stable multidimensional shocks. Zbl 1029.35171
Coulombel, Jean-François
2002
Note on a paper by Robinet, Gressier, Casalis and Moschetta. Zbl 1152.76394
Coulombel, Jean-François; Benzoni-Gavage, Sylvie; Serre, Denis
2002
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#### Cited by 252 Authors

 20 Coulombel, Jean-François 17 Morando, Alessandro 15 Trakhinin, Yuri L. 15 Trebeschi, Paola 14 Secchi, Paolo 13 Ducomet, Bernard 11 Nečasová, Šárka 9 Chalons, Christophe 7 Xie, Feng 6 Benzoni-Gavage, Sylvie 6 Berthon, Christophe 6 Goudon, Thierry 6 Li, Dening 6 Peng, Yuejun 5 Benoit, Antoine 5 Jiang, Peng 5 Ruan, Lizhi 5 Wang, Tao 5 Wang, Ya-Guang 5 Williams, Mark 5 Xiang, Wei 4 Carrillo de la Plata, José Antonio 4 Choi, Young-Pil 4 Coquel, Frédéric 4 Klar, Axel 4 Lin, Chunjin 4 Rohde, Christian 4 Tse, Oliver 4 Wang, Dehua 4 Wang, Wenjun 4 Wasiolek, Victor 4 Yu, Fang 3 Catania, Davide 3 Chen, Gui-Qiang G. 3 Chen, Robin Ming 3 Chen, Shuxing 3 Danchin, Raphaël 3 Després, Bruno 3 Fan, Lili 3 Hu, Jilong 3 Plaza, Ramón G. 3 Qin, Yuming 3 Samaey, Giovanni 3 Schneider, Florian H. 3 Turpault, Rodolphe 3 Xu, Jiang 2 Ambroso, Annalisa 2 Audiard, Corentin 2 Calvo, Juan G. 2 D’Abbicco, Marcello 2 Fang, Beixiang 2 Feng, Baowei 2 Foucher, Françoise 2 Franck, Emmanuel 2 Frank, Martin 2 Freistühler, Heinrich 2 Godlewski, Edwige 2 Gu, Xumin 2 Guès, Olivier 2 Hauck, Cory D. 2 Hérard, Jean-Marc 2 Huang, Feimin 2 Kabil, Buğra 2 Lafitte, Pauline 2 Lagoutière, Frédéric 2 Massot, Marc 2 Melis, Ward 2 Nguyen, Toan Trong 2 Pierre, Olivier 2 Renac, Florent 2 Seguin, Nicolas 2 Shkoller, Steve 2 Wang, Jing 2 Wang, Wei 2 Wang, Yaguang 2 Wang, Yanjin 2 Yong, Wen-An 2 Yuan, Difan 2 Zhang, Ming 2 Zhang, Zhifei 2 Zumbrun, Kevin R. 1 Addala, Lanoir 1 Agarwal, Ravi P. 1 Aguillon, Nina 1 Alazard, Thomas 1 Aregba-Driollet, Denise 1 Ashyralyev, Allaberen 1 Beauchard, Karine 1 Beirão da Veiga, Hugo 1 Bernier, Joackim 1 Berthelin, Florent 1 Besse, Christophe 1 Bianchini, Roberta 1 Boileau, Matthieu 1 Borsche, Raul 1 Bouchut, François 1 Boudin, Laurent 1 Brahimi, Sihame 1 Brooks, Gregory P. 1 Brull, Stephane ...and 152 more Authors
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#### Cited in 81 Serials

 21 Journal of Differential Equations 18 Archive for Rational Mechanics and Analysis 13 SIAM Journal on Mathematical Analysis 11 Journal of Computational Physics 10 Journal of Hyperbolic Differential Equations 7 Mathematical Methods in the Applied Sciences 6 Journal of Mathematical Analysis and Applications 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Discrete and Continuous Dynamical Systems 6 Communications on Pure and Applied Analysis 5 Mathematics of Computation 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Computers and Fluids 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Quarterly of Applied Mathematics 4 Communications in Partial Differential Equations 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Physica D 3 Numerical Methods for Partial Differential Equations 3 Journal of Scientific Computing 3 Journal of Mathematical Fluid Mechanics 3 Nonlinear Analysis. Real World Applications 2 Applicable Analysis 2 Communications in Mathematical Physics 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Physics 2 Nonlinearity 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Calcolo 2 Indiana University Mathematics Journal 2 Mathematische Annalen 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Applied Mathematics Letters 2 Asymptotic Analysis 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Evolution Equations 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Analysis and Applications (Singapore) 2 Discrete and Continuous Dynamical Systems. Series S 2 Kinetic and Related Models 2 International Journal of Differential Equations 2 Journal of Pseudo-Differential Operators and Applications 2 Séminaire Laurent Schwartz. EDP et Applications 1 Computers & Mathematics with Applications 1 Journal of the Mechanics and Physics of Solids 1 Acta Mathematica Vietnamica 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik 1 Zeitschrift für Analysis und ihre Anwendungen 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 Applied Mathematical Modelling 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Journal of Mathematical Sciences (New York) 1 The Journal of Fourier Analysis and Applications 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Discrete and Continuous Dynamical Systems. Series B 1 Multiscale Modeling & Simulation 1 Journal of the Institute of Mathematics of Jussieu 1 Boundary Value Problems 1 Communications in Mathematical Analysis 1 Communications in Computational Physics 1 Networks and Heterogeneous Media 1 Confluentes Mathematici 1 Advances in Mathematical Physics 1 Science China. Mathematics 1 Journal of Function Spaces 1 Journal de l’École Polytechnique – Mathématiques 1 SMAI Journal of Computational Mathematics
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#### Cited in 24 Fields

 207 Partial differential equations (35-XX) 157 Fluid mechanics (76-XX) 39 Numerical analysis (65-XX) 23 Optics, electromagnetic theory (78-XX) 16 Statistical mechanics, structure of matter (82-XX) 15 Mechanics of deformable solids (74-XX) 10 Classical thermodynamics, heat transfer (80-XX) 4 Biology and other natural sciences (92-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Probability theory and stochastic processes (60-XX) 3 Astronomy and astrophysics (85-XX) 3 Operations research, mathematical programming (90-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)