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## Perthame, Benoît

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 Author ID: perthame.benoit Published as: Perthame, B.; Perthame, Benoit; Perthame, Benoît; Perthame, Benôıt External Links: MGP · Wikidata · GND
 Documents Indexed: 272 Publications since 1984, including 5 Books
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#### Co-Authors

 34 single-authored 20 Souganidis, Panagiotis E. 14 Lions, Pierre-Louis 12 Golse, François 11 Salort, Delphine 10 Tang, Min 10 Vauchelet, Nicolas 9 Jabin, Pierre-Emmanuel 9 Markowich, Peter Alexander 9 Mirrahimi, Sepideh 8 Lorz, Alexander 7 Barles, Guy 7 Bouchut, François 7 Calvez, Vincent 7 Clairambault, Jean 7 Mischler, Stéphane 7 Ryzhik, Lenya 6 Bardos, Claude Williams 5 Doumic, Marie 5 Le Tallec, Patrick 5 Zubelli, Jorge P. 4 Bristeau, Marie-Odile 4 Carrillo de la Plata, José Antonio 4 Castella, François 4 Coquel, Frédéric 4 Corrias, Lucilla 4 Nadin, Grégoire 4 Sentis, Remi 4 Stevens, Angela 4 Tadmor, Eitan 4 Vega, Luis 3 Andries, Pierre 3 Audusse, Emmanuel 3 Bourgat, Jean-François 3 Chen, Gui-Qiang G. 3 Godlewski, Edwige 3 Katsaounis, Theodoros 3 Laurençot, Philippe 3 Lorenzi, Tommaso 3 Michel, Philippe 3 Pakdaman, Khashayar 3 Qiu, Youchun 3 Quirós Gracián, Fernando 3 Rascle, Paul 3 Schmeiser, Christian 3 Simeoni, Chiara 3 Yasuda, Shugo 2 Bardi, Martino 2 Bekkal-Brikci, Fadia 2 Benamou, Jean-David 2 Berestycki, Henri 2 Bouin, Emeric 2 Bourdarias, Christian 2 Bournaveas, Nikolaos 2 Bubba, Federica 2 Cáceres, María-José 2 Cheddadi, Ibrahim 2 Deslys, Jean-Philippe 2 Després, Bruno 2 DiBenedetto, Emmanuele 2 Dolbeault, Jean 2 Drasdo, Dirk 2 El Amine, Khalid 2 Escobedo Martínez, Miguel 2 Esteban, Maria J. 2 Gasser, Ingenuin 2 Gerbeau, Jean-Frédéric 2 Gwiazda, Piotr 2 Haskovec, Jan 2 Herrero, Henar 2 James, François 2 Kang, Kyungkeun 2 Lenuzza, Natacha 2 Lucquin-Desreux, Brigitte 2 Makridakis, Charalambos G. 2 Marciniak-Czochra, Anna K. 2 Marrocco, Americo 2 Mellet, Antoine 2 Moussa, Ayman 2 Mouthon, Franck 2 Pouchol, Camille 2 Pulvirenti, Mario 2 Ribes, Edouard 2 Sainte-Marie, Jacques 2 Seguin, Nicolas 2 Stoufflet, Bruno 2 Sun, Weiran 2 Taing, Cécile 2 Tournus, Magali 2 Vasseur, Alexis F. 2 Vazquez, Juan Luis 2 Velázquez, Juan J. L. 2 Vignon-Clementel, Irene E. 2 Wakano, Joe Yuichiro 2 Zaag, Hatem 1 Almeida, Luis A. F. 1 Almeida, Luis Tadeu 1 Aoki, Kazuo 1 Batt, Jürgen 1 Belhadj, Mohamed 1 Bellomo, Nicola ...and 93 more Co-Authors
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#### Serials

 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Comptes Rendus de l’Académie des Sciences. Série I 10 Archive for Rational Mechanics and Analysis 7 Journal of Differential Equations 7 Communications in Partial Differential Equations 6 Communications in Mathematical Physics 6 SIAM Journal on Numerical Analysis 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Communications in Mathematical Sciences 5 Journal of Mathematical Biology 5 Nonlinearity 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 SIAM Journal on Mathematical Analysis 4 Communications on Pure and Applied Mathematics 4 Journal of Functional Analysis 4 Chinese Annals of Mathematics. Series B 4 Mathematical and Computer Modelling 4 Asymptotic Analysis 4 Mathematical Modelling of Natural Phenomena 4 Kinetic and Related Models 3 Mathematics of Computation 3 Transactions of the American Mathematical Society 3 Revista Matemática Iberoamericana 3 SIAM Journal on Applied Mathematics 3 Interfaces and Free Boundaries 3 Oberwolfach Reports 2 Computers & Mathematics with Applications 2 Inverse Problems 2 Journal of Computational Physics 2 Journal of Statistical Physics 2 Mathematical Biosciences 2 Mathematical Methods in the Applied Sciences 2 Transport Theory and Statistical Physics 2 Bulletin of Mathematical Biology 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Numerische Mathematik 2 Japan Journal of Applied Mathematics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Séminaire Équations aux Dérivées Partielles 2 Methods and Applications of Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Journal of Biological Dynamics 2 Networks and Heterogeneous Media 2 The Journal of Mathematical Neuroscience 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Nonlinear Analysis. Theory, Methods & Applications 1 Applicable Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Analysis and Applications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Optimization 1 BIT 1 Calcolo 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Control and Optimization 1 Theoretical Population Biology 1 Acta Applicandae Mathematicae 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Applied Mathematics Letters 1 Journal of the American Mathematical Society 1 European Journal of Mechanics. B. Fluids 1 Applications of Mathematics 1 Geometric and Functional Analysis. GAFA 1 European Journal of Operational Research 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Advances in Mathematical Sciences and Applications 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of the Egyptian Mathematical Society 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Markov Processes and Related Fields 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 European Journal of Mechanics. B. Fluids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Milan Journal of Mathematics 1 Mathematical Medicine and Biology 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oxford Lecture Series in Mathematics and its Applications 1 Series on Advances in Mathematics for Applied Sciences 1 Journal of Theoretical Biology 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 1 SIAM/ASA Journal on Uncertainty Quantification 1 Séminaire Laurent Schwartz. EDP et Applications 1 Philosophical Transactions A. Royal Society of London 1 Frontiers in Mathematics 1 Lecture Notes on Mathematical Modelling in the Life Sciences ...and 2 more Serials
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#### Fields

 209 Partial differential equations (35-XX) 115 Biology and other natural sciences (92-XX) 77 Fluid mechanics (76-XX) 53 Statistical mechanics, structure of matter (82-XX) 37 Numerical analysis (65-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 18 Integral equations (45-XX) 11 Operator theory (47-XX) 10 Ordinary differential equations (34-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Probability theory and stochastic processes (60-XX) 7 Mechanics of deformable solids (74-XX) 7 Astronomy and astrophysics (85-XX) 5 General and overarching topics; collections (00-XX) 5 Quantum theory (81-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 4 Systems theory; control (93-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

236 Publications have been cited 6,320 times in 3,554 Documents Cited by Year
Transport equations in biology. Zbl 1185.92006
Perthame, Benoît
2007
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. Zbl 1133.65308
Audusse, Emmanuel; Bouchut, François; Bristeau, Marie-Odile; Klein, Rupert; Perthame, Benoît
2004
Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system. Zbl 0741.35061
Lions, P. L.; Perthame, B.
1991
Regularity of the moments of the solution of a transport equation. Zbl 0652.47031
Golse, François; Lions, Pierre-Louis; Perthame, Benoît; Sentis, Rémi
1988
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions. Zbl 1112.35023
Blanchet, Adrien; Dolbeault, Jean; Perthame, Benoit
2006
A kinetic formulation of multidimensional scalar conservation laws and related equations. Zbl 0820.35094
Lions, P. L.; Perthame, B.; Tadmor, E.
1994
Global solutions of some chemotaxis and angiogenesis system in high space dimension. Zbl 1115.35136
Corrias, L.; Perthame, Benoît; Zaag, H.
2004
Kinetic formulation of the isentropic gas dynamics and $$p$$-systems. Zbl 0799.35151
Lions, P. L.; Perthame, B.; Tadmor, E.
1994
Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Zbl 0853.76077
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
1996
Kinetic formulation of conservation laws. Zbl 1030.35002
Perthame, Benoît
2002
Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. Zbl 0997.76023
Gerbeau, J.-F.; Perthame, B.
2001
Kinetic models for chemotaxis and their drift-diffusion limits. Zbl 1052.92005
Chalub, Fabio A. C. C.; Markowich, Peter A.; Perthame, Benoît; Schmeiser, Christian
2004
A kinetic scheme for the Saint-Venant system with a source term. Zbl 1008.65066
Perthame, B.; Simeoni, C.
2001
General relative entropy inequality: an illustration on growth models. Zbl 1085.35042
Michel, Philippe; Mischler, Stéphane; Perthame, Benoît
2005
The non-local Fisher-KPP equation: travelling waves and steady states. Zbl 1195.35088
Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya
2009
Exit time problems in optimal control and vanishing viscosity method. Zbl 0674.49027
Barles, G.; Perthame, B.
1988
Optimal critical mass in the two dimensional Keller-Segel model in $$R^2$$. Zbl 1056.35076
Dolbeault, Jean; Perthame, Benoît
2004
Derivation of hyperbolic models for chemosensitive movement. Zbl 1080.92014
Filbet, Francis; Laurençot, Philippe; Perthame, Benoît
2005
Discontinuous solutions of deterministic optimal stopping time problems. Zbl 0629.49017
Barles, G.; Perthame, B.
1987
The dynamics of adaptation: An illuminating example and a Hamilton–Jacobi approach. Zbl 1072.92035
Diekmann, Odo; Jabin, Pierre-Emanuel; Mischler, Stéphane; Perthame, Benoît
2005
The Gaussian-BGK model of Boltzmann equation with small Prandtl number. Zbl 0967.76082
Andries, Pierre; Le Tallec, Patrick; Perlat, Jean-Philippe; Perthame, Benoît
2000
Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. Zbl 0744.76088
Perthame, B.
1992
Global existence to the BGK model of Boltzmann equation. Zbl 0694.35134
Perthame, B.
1989
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations. Zbl 1031.35077
Chen, Gui-Qiang; Perthame, Benoît
2003
Kruzkov’s estimates for scalar conservation laws revisited. Zbl 0955.65069
Bouchut, F.; Perthame, B.
1998
On positivity preserving finite volume schemes for Euler equations. Zbl 0857.76062
Perthame, Benoit; Shu, Chi-Wang
1996
Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. Zbl 0960.76051
Coquel, Frédéric; Perthame, Benoît
1998
A consistent BGK-type model for gas mixtures. Zbl 1001.82093
Andries, Pierre; Aoki, Kazuo; Perthame, Benoit
2002
A kinetic equation with kinetic entropy functions for scalar conservation laws. Zbl 0729.76070
1991
Boltzmann type schemes for gas dynamics and the entropy property. Zbl 0714.76078
Perthame, B.
1990
Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d’un opérateur de transport. (A compactness result for transport equations and application to the calculus of the limit of the principal eigenvalue of a transport operator). Zbl 0591.45007
Golse, François; Perthame, Benoît; Sentis, Rémi
1985
Exponential decay for the fragmentation or cell-division equation. Zbl 1072.35195
Perthame, Benoît; Ryzhik, Lenya
2005
PDE models for chemotactic movements: parabolic, hyperbolic and kinetic. Zbl 1099.35157
Perthame, Benoît
2004
A chemotaxis model motivated by angiogenesis. Zbl 1028.35062
Corrias, L.; Perthame, B.; Zaag, H.
2003
Gelation in coagulation and fragmentation models. Zbl 1016.82027
Escobedo, M.; Mischler, S.; Perthame, B.
2002
The nonaccretive radiative transfer equations: Existence of solutions and Rosseland approximation. Zbl 0655.35075
Bardos, C.; Golse, F.; Perthame, B.; Sentis, R.
1988
Morrey-Campanato estimates for Helmholtz equations. Zbl 0932.35048
Perthame, Benoit; Vega, Luis
1999
Dirac mass dynamics in multidimensional nonlocal parabolic equations. Zbl 1229.35113
Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoît
2011
A Fourier spectral method for homogeneous Boltzmann equations. Zbl 0870.76074
Pareschi, Lorenzo; Perthame, Benoit
1996
On a boundary layer problem for the nonlinear Boltzmann equation. Zbl 0668.76089
Golse, Francois; Perthame, Benoit; Sulem, Catherine
1988
Dirac concentrations in Lotka-Volterra parabolic PDEs. Zbl 1172.35005
Perthame, Benoit; Barles, Guy
2008
Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure. Zbl 0919.35088
Perthame, B.
1998
Gelation and mass conservation in coagulation-fragmentation models. Zbl 1133.82316
Escobedo, M.; Laurençot, Ph.; Mischler, S.; Perthame, B.
2003
Equilibrium schemes for scalar conservation laws with stiff sources. Zbl 1017.65070
Botchorishvili, Ramaz; Perthame, Benoit; Vasseur, Alexis
2003
A numerical method using upwind schemes for the resolution of two-phase flows. Zbl 0893.76052
Coquel, F.; El Amine, K.; Godlewski, E.; Perthame, B.; Rascle, P.
1997
Time decay, propagation of low moments and dispersive effects for kinetic equations. Zbl 0852.35139
Perthame, B.
1996
Numerical passage from kinetic to fluid equations. Zbl 0718.76086
Coron, F.; Perthame, B.
1991
The Hele-Shaw asymptotics for mechanical models of tumor growth. Zbl 1293.35347
Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis
2014
Mathematical tools for kinetic equations. Zbl 1151.82351
Perthame, Benoît
2004
A limiting case for velocity averaging. Zbl 0956.45010
Perthame, B.; Souganidis, P. E.
1998
Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies. Zbl 1071.35079
Audusse, Emmanuel; Perthame, Benoît
2005
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. Zbl 1274.92025
Lorz, Alexander; Lorenzi, Tommaso; Hochberg, Michael E.; Clairambault, Jean; Perthame, Benoît
2013
Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states. Zbl 1259.35198
Cáceres, María J.; Carrillo, José A.; Perthame, Benoît
2011
Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Zbl 1253.35186
Bouin, Emeric; Calvez, Vincent; Meunier, Nicolas; Mirrahimi, Sepideh; Perthame, Benoît; Raoul, Gaël; Voituriez, Raphaël
2012
Microreversible collisions for polyatomic gases and Boltzmann’s theorem. Zbl 0807.76067
Bourgat, J.-F.; Desvillettes, L.; Le Tallec, P.; Perthame, B.
1994
Weighted $$L^ \infty$$ bounds and uniqueness for the Boltzmann BGK model. Zbl 0786.76072
Perthame, B.; Pulvirenti, M.
1993
Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations. Zbl 0691.49028
Barles, G.; Perthame, B.
1990
Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. Zbl 1334.92204
Lorz, Alexander; Lorenzi, Tommaso; Clairambault, Jean; Escargueil, Alexandre; Perthame, Benoît
2015
Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Zbl 1204.35027
Barles, Guy; Mirrahimi, Sepideh; Perthame, Benoît
2009
Dynamics of a structured neuron population. Zbl 1267.35239
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2010
General entropy equations for structured population models and scattering. Zbl 1049.35070
Michel, Philippe; Mischler, Stéphane; Perthame, Benoît
2004
On spherical symmetry solutions of the Euler-Poisson equation for the evolution of gaseous stars. Zbl 0743.35048
Makino, Tetu; Perthame, Benoît
1990
Scalar conservation laws with rough (stochastic) fluxes. Zbl 1333.60140
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2013
A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows. Zbl 1044.35056
Bouchut, François; Mangeney-Castelnau, Anne; Perthame, Benoît; Vilotte, Jean-Pierre
2003
Stability in a nonlinear population maturation model. Zbl 1020.92025
Mischler, Stéphane; Perthame, Benoît; Ryzhik, Lenya
2002
Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces. Zbl 1134.92006
Corrias, Lucilla; Perthame, Benoît
2008
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. Zbl 1290.35194
Audusse, Emmanuel; Bristeau, Marie-Odile; Perthame, Benoît; Sainte-Marie, Jacques
2011
Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases. Zbl 1101.76377
Andries, Pierre; Bourgat, Jean-François; le Tallec, Patrick; Perthame, Benoit
2002
Existence of solutions of the hyperbolic Keller-Segel model. Zbl 1180.35343
Perthame, Benoît; Dalibard, Anne-Laure
2009
Coupling Boltzmann and Euler equations without overlapping. Zbl 0796.76063
Bourgat, J. F.; Le Tallec, P.; Perthame, B.; Qiu, Y.
1994
Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case. Zbl 1323.35233
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2014
Exponential decay for the growth-fragmentation/cell-division equations. Zbl 1183.35038
Laurençot, Philippe; Perthame, Benoit
2009
Strichartz’ estimates for kinetic transport equations. Zbl 0848.35095
Castella, François; Perthame, Benoît
1996
Non-existence of global solutions to Euler-Poisson equations for repulsive forces. Zbl 0717.35049
Perthame, Benoît
1990
Relaxation and self-sustained oscillations in the time elapsed neuron network model. Zbl 1278.82046
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2013
Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Zbl 1337.35077
Perthame, Benoît; Génieys, Stephane
2007
Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. Zbl 1137.49027
Barles, Guy; Perthame, Benoît
2007
Regularity and propagation of moments in some nonlinear Vlasov systems. Zbl 0984.35102
Gasser, I.; Jabin, P.-E.; Perthame, B.
2000
A MUSCL method satisfying all the numerical entropy inequalities. Zbl 0853.65091
Bouchut, F.; Bourdarias, Ch.; Perthame, B.
1996
Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation. Zbl 1219.35038
Nadin, Grégoire; Perthame, Benoît; Tang, Min
2011
Boltzmann equation with infinite energy: Renormalized solutions and distributional solutions for small initial data and initial data close to a Maxwellian. Zbl 0889.35077
Mischler, S.; Perthame, B.
1997
Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians. Zbl 0688.35052
Lions, P. L.; Perthame, B.
1987
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. Zbl 1280.34066
Nadin, G.; Rossi, L.; Ryzhik, L.; Perthame, B.
2013
Prion dynamics with size dependency-strain phenomena. Zbl 1315.92039
Calvez, V.; Lenuzza, N.; Doumic, M.; Deslys, J.-P.; Mouthon, F.; Perthame, B.
2010
Traveling waves for the Keller-Segel system with Fisher birth terms. Zbl 1154.35459
Nadin, Gregoire; Perthame, Benoît; Ryzhik, Lenya
2008
An age-and-cyclin-structured cell population model for healthy and tumoral tissues. Zbl 1148.92014
Brikci, Fadia Bekkal; Clairambault, Jean; Ribba, Benjamin; Perthame, Benoît
2008
On the inverse problem for a size-structured population model. Zbl 1118.35072
Perthame, Benoît; Zubelli, Jorge P.
2007
Some new Godunov and relaxation methods for two-phase flow problems. Zbl 1064.76545
Coquel, F.; Godlewski, E.; Perthame, B.; In, A.; Rascle, P.
2001
Lemmes de moments, de moyenne et de dispersion. (Moments, averaging and dispersion lemmas). Zbl 0761.35085
Lions, Pierre-Louis; Perthame, Benoît
1992
The Rosseland approximation for the radiative transfer equations. Zbl 0654.65095
Bardos, C.; Golse, F.; Perthame, B.
1987
Generalized solutions of the radiative transfer equations in a singular case. Zbl 0614.35084
Golse, F.; Perthame, B.
1986
Upwinding of the source term at interfaces for Euler equations with high friction. Zbl 1213.76123
Bouchut, Francois; Ounaissa, Haythem; Perthame, Benoît
2007
Modified Keller-Segel system and critical mass for the log interaction kernel. Zbl 1126.35077
Calvez, Vincent; Perthame, Benoît; Sharifi tabar, Mohsen
2007
On the modified Enskog equation for elastic and inelastic collisions. Models with spin. Zbl 0850.70141
Esteban, Maria J.; Perthame, Benoît
1991
Conservative cross diffusions and pattern formation through relaxation. Zbl 1179.35156
Bendahmane, Mostafa; Lepoutre, Thomas; Marrocco, Americo; Perthame, Benoît
2009
Size distribution dependence of prion aggregates infectivity. Zbl 1161.92033
Calvez, Vincent; Lenuzza, Natacha; Oelz, Dietmar; Deslys, Jean-Philippe; Laurent, Pascal; Mouthon, Franck; Perthame, Benoît
2009
Line-energy Ginzburg-Landau models: zero-energy states. Zbl 1072.35051
Otto, Felix; Jabin, Pierre-Emmanuel; Perthame, Benoît
2002
High frequency limit of the Helmholtz equations. Zbl 1090.35165
Benamou, Jean-David; Castella, François; Katsaounis, Theodoros; Perthame, Benoit
2002
A BGK model for small Prandtl number in the Navier-Stokes approximation. Zbl 0943.76500
Bouchut, François; Perthame, Benoît
1993
Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. Zbl 1333.92009
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2014
Hele-Shaw limit for a system of two reaction-(Cross-)diffusion equations for living tissues. Zbl 1435.35390
Bubba, Federica; Perthame, Benoît; Pouchol, Camille; Schmidtchen, Markus
2020
The flux limited Keller-Segel system; properties and derivation from kinetic equations. Zbl 1441.35056
Perthame, Benoît; Vauchelet, Nicolas; Wang, Zhian
2020
Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations. Zbl 1423.35177
Almeida, Luis; Bubba, Federica; Perthame, Benoît; Pouchol, Camille
2019
A two-species hyperbolic-parabolic model of tissue growth. Zbl 1425.35198
Gwiazda, Piotr; Perthame, Benoît; Świerczewska-Gwiazda, Agnieszka
2019
Implicit and semi-implicit numerical schemes for the gradient flow of the formation of biological transport networks. Zbl 1437.65095
Fang, Di; Jin, Shi; Markowich, Peter; Perthame, Benoît
2019
Derivation of a voltage density equation from a voltage-conductance kinetic model for networks of integrate-and-fire neurons. Zbl 1433.35429
Perthame, Benoît; Salort, Delphine
2019
Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller-Segel equation. Zbl 1397.92101
Perthame, Benoît; Yasuda, Shugo
2018
Dynamics of concentration in a population model structured by age and a phenotypical trait. Zbl 1398.35251
Nordmann, Samuel; Perthame, Benoît; Taing, Cécile
2018
Traveling wave and aggregation in a flux-limited Keller-Segel model. Zbl 1405.92030
Calvez, Vincent; Perthame, Benoît; Yasuda, Shugo
2018
The fractional diffusion limit of a kinetic model with biochemical pathway. Zbl 1395.35015
Perthame, Benoît; Sun, Weiran; Tang, Min
2018
Super-linear propagation for a general, local cane toads model. Zbl 1407.35112
Henderson, Christopher; Perthame, Benoît; Souganidis, Panagiotis E.
2018
Long-time asymptotics for polymerization models. Zbl 1400.82316
Calvo, Juan; Doumic, Marie; Perthame, Benoît
2018
A Hele-Shaw problem for tumor growth. Zbl 1377.35245
Mellet, Antoine; Perthame, Benoît; Quirós, Fernando
2017
On interfaces between cell populations with different mobilities. Zbl 1359.35204
Lorenzi, Tommaso; Lorz, Alexander; Perthame, Benoît
2017
Toward an integrated workforce planning framework using structured equations. Zbl 1403.90462
Doumic, Marie; Perthame, Benoît; Ribes, Edouard; Salort, Delphine; Toubiana, Nathan
2017
Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway. Zbl 1358.35207
Perthame, Benoît; Tang, Min; Vauchelet, Nicolas
2016
Notes on a PDE system for biological network formation. Zbl 1334.35101
Haskovec, Jan; Markowich, Peter; Perthame, Benoît; Schlottbom, Matthias
2016
Rare mutations limit of a steady state dispersal evolution model. Zbl 1387.35027
Perthame, Benoit; Souganidis, P. E.
2016
Uncertainty propagation; intrusive kinetic formulations of scalar conservation laws. Zbl 1362.35342
Despres, Bruno; Perthame, Benoit
2016
Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes. Zbl 1345.60069
Gess, Benjamin; Perthame, Benoît; Souganidis, Panagiotis E.
2016
Free boundary problems for tumor growth: a viscosity solutions approach. Zbl 1334.35360
Kim, Inwon C.; Perthame, Benoît; Souganidis, Panagiotis E.
2016
Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. Zbl 1334.92204
Lorz, Alexander; Lorenzi, Tommaso; Clairambault, Jean; Escargueil, Alexandre; Perthame, Benoît
2015
Parabolic equations in biology. Growth, reaction, movement and diffusion. Zbl 1333.35001
Perthame, Benoît
2015
Asymptotic analysis of a selection model with space. Zbl 1327.35011
Mirrahimi, Sepideh; Perthame, Benoît
2015
Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience. Zbl 1336.35332
Carrillo, José Antonio; Perthame, Benoît; Salort, Delphine; Smets, Didier
2015
Mathematical analysis of a PDE system for biological network formation. Zbl 1345.35120
Haskovec, Jan; Markowich, Peter; Perthame, Benoit
2015
Incompressible limit of a mechanical model of tumour growth with viscosity. Zbl 1353.35294
Perthame, Benoît; Vauchelet, Nicolas
2015
Time fluctuations in a population model of adaptive dynamics. Zbl 1312.35011
Mirrahimi, Sepideh; Perthame, Benoît; Souganidis, Panagiotis E.
2015
A simple derivation of BV bounds for inhomogeneous relaxation systems. Zbl 1316.35183
Perthame, Benoît; Seguin, Nicolas; Tournus, Magali
2015
Data assimilation for hyperbolic conservation laws: a Luenberger observer approach based on a kinetic description. Zbl 1329.35195
Boulanger, Anne-Celine; Moireau, Philippe; Perthame, Benoît; Sainte-Marie, Jacques
2015
Dynamics of time elapsed inhomogeneous neuron network model. Zbl 1337.92014
Kang, Moon-Jin; Perthame, Benoît; Salort, Delphine
2015
Competition and boundary formation in heterogeneous media: application to neuronal differentiation. Zbl 1325.35237
Perthame, Benoît; Quiñinao, Cristóbal; Touboul, Jonathan
2015
Transversal instability for the thermodiffusive reaction-diffusion system. Zbl 1328.35097
Kowalczyk, Michal; Perthame, Benoît; Vauchelet, Nicolas
2015
The Hele-Shaw asymptotics for mechanical models of tumor growth. Zbl 1293.35347
Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis
2014
Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case. Zbl 1323.35233
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2014
Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. Zbl 1333.92009
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2014
Derivation of a Hele-Shaw type system from a cell model with active motion. Zbl 1325.35092
Perthame, Benoît; Quirós, Fernando; Tang, Min; Vauchelet, Nicholas
2014
Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient. Zbl 1366.92065
Perthame, Benoît; Tang, Min; Vauchelet, Nicolas
2014
Direct competition results from strong competition for limited resource. Zbl 1293.35346
Mirrahimi, Sepideh; Perthame, Benoît; Wakano, Joe Yuichiro
2014
Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity. Zbl 1412.92001
Cáceres, María J.; Perthame, Benoît
2014
Some mathematical aspects of tumor growth and therapy. Zbl 1373.35322
Perthame, Benoît
2014
Long-term behaviour of phenotypically structured models. Zbl 1371.92087
Lorz, Alexander; Perthame, Benoît
2014
Composite waves for a cell population system modeling tumor growth and invasion. Zbl 1321.35249
Tang, Min; Vauchelet, Nicolas; Cheddadi, Ibrahim; Vignon-Clementel, Irene; Drasdo, Dirk; Perthame, Benoît
2014
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. Zbl 1274.92025
Lorz, Alexander; Lorenzi, Tommaso; Hochberg, Michael E.; Clairambault, Jean; Perthame, Benoît
2013
Scalar conservation laws with rough (stochastic) fluxes. Zbl 1333.60140
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2013
Relaxation and self-sustained oscillations in the time elapsed neuron network model. Zbl 1278.82046
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2013
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. Zbl 1280.34066
Nadin, G.; Rossi, L.; Ryzhik, L.; Perthame, B.
2013
Stochastic averaging lemmas for kinetic equations. Zbl 1323.35234
Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E.
2013
Optimal regularizing effect for scalar conservation laws. Zbl 1288.35343
Golse, François; Perthame, Benoît
2013
Composite waves for a cell population system modeling tumor growth and invasion. Zbl 1346.92017
Tang, Min; Vauchelet, Nicolas; Cheddadi, Ibrahim; Vignon-Clementel, Irene; Drasdo, Dirk; Perthame, Benoît
2013
On a voltage-conductance kinetic system for integrate & fire neural networks. Zbl 1284.35103
Perthame, Benoît; Salort, Delphine
2013
Nonlinear stability of a Vlasov equation for magnetic plasmas. Zbl 1262.35197
Charles, Frédérique; Després, Bruno; Perthame, Benoît; Sentis, Rémis
2013
Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Zbl 1253.35186
Bouin, Emeric; Calvez, Vincent; Meunier, Nicolas; Mirrahimi, Sepideh; Perthame, Benoît; Raoul, Gaël; Voituriez, Raphaël
2012
Evolution of species trait through resource competition. Zbl 1279.92060
Mirrahimi, Sepideh; Perthame, Benoît; Wakano, Joe Yuichiro
2012
Regularization in Keller-Segel type systems and the De Giorgi method. Zbl 1288.35146
Perthame, Benoît; Vasseur, Alexis
2012
Analysis of a simplified model of the urine concentration mechanism. Zbl 1262.35204
Tournus, Magali; Edwards, Aurélie; Seguin, Nicolas; Perthame, Benoît
2012
A singular Hamilton-Jacobi equation modeling the tail problem. Zbl 1280.35007
Mirrahimi, Sepideh; Barles, Guy; Perthame, Benoît; Souganidis, Panagiotis E.
2012
Corrigendum to “An integro-differential equation model for alignment and orientational aggregation” [J. Differential Equations 246 (4) (2009) 1387-1421]. Zbl 1236.47045
Kang, Kyungkeun; Perthame, Benoit; Stevens, Angela; Velázquez, J. J. L.
2012
Dirac mass dynamics in multidimensional nonlocal parabolic equations. Zbl 1229.35113
Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoît
2011
Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states. Zbl 1259.35198
Cáceres, María J.; Carrillo, José A.; Perthame, Benoît
2011
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. Zbl 1290.35194
Audusse, Emmanuel; Bristeau, Marie-Odile; Perthame, Benoît; Sainte-Marie, Jacques
2011
Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation. Zbl 1219.35038
Nadin, Grégoire; Perthame, Benoît; Tang, Min
2011
Travelling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities. Zbl 1223.35102
Perthame, Benoît; Schmeiser, Christian; Tang, Min; Vauchelet, Nicolas
2011
A structured population model of cell differentiation. Zbl 1235.35030
Doumic, Marie; Marciniak-Czochra, Anna; Perthame, Benoît; Zubelli, Jorge P.
2011
Waves for a hyperbolic Keller–Segel model and branching instabilities. Zbl 1221.35088
Cerreti, Fiammetta; Perthame, Benoît; Schmeiser, Christian; Tang, Min; Vauchelet, Nicolas
2011
Population formulation of adaptative meso-evolution: theory and numerics. Zbl 1379.92052
Mirrahimi, Sepideh; Perthame, Benoît; Bouin, Emeric; Millien, Pierre
2011
A homogenization approach to flashing ratchets. Zbl 1209.35013
Perthame, Benoît; Souganidis, Panagiotis E.
2011
Dynamics of a structured neuron population. Zbl 1267.35239
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine
2010
Prion dynamics with size dependency-strain phenomena. Zbl 1315.92039
Calvez, V.; Lenuzza, N.; Doumic, M.; Deslys, J.-P.; Mouthon, F.; Perthame, B.
2010
Models of self-organizing bacterial communities and comparisons with experimental observations. Zbl 1184.35158
Marrocco, A.; Henry, H.; Holland, I. B.; Plapp, M.; Séror, S. J.; Perthame, B.
2010
Stability analysis of a simplified yet complete model for chronic myelogenous leukemia. Zbl 1203.92036
Doumic-Jauffret, Marie; Kim, Peter S.; Perthame, Benoît
2010
Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations. Zbl 1196.92031
Perthame, Benoît; Gauduchon, Mathias
2010
The non-local Fisher-KPP equation: travelling waves and steady states. Zbl 1195.35088
Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya
2009
Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Zbl 1204.35027
Barles, Guy; Mirrahimi, Sepideh; Perthame, Benoît
2009
Existence of solutions of the hyperbolic Keller-Segel model. Zbl 1180.35343
Perthame, Benoît; Dalibard, Anne-Laure
2009
Exponential decay for the growth-fragmentation/cell-division equations. Zbl 1183.35038
Laurençot, Philippe; Perthame, Benoit
2009
Conservative cross diffusions and pattern formation through relaxation. Zbl 1179.35156
Bendahmane, Mostafa; Lepoutre, Thomas; Marrocco, Americo; Perthame, Benoît
2009
Size distribution dependence of prion aggregates infectivity. Zbl 1161.92033
Calvez, Vincent; Lenuzza, Natacha; Oelz, Dietmar; Deslys, Jean-Philippe; Laurent, Pascal; Mouthon, Franck; Perthame, Benoît
2009
Numerical solution of an inverse problem in size-structured population dynamics. Zbl 1161.92020
Doumic, Marie; Perthame, Benoît; Zubelli, Jorge P.
2009
Large-time behavior of periodic entropy solutions to anisotropic degenerate parabolic-hyperbolic equations. Zbl 1176.35031
Chen, Gui-Qiang; Perthame, Benoît
2009
An integro-differential equation model for alignment and orientational aggregation. Zbl 1157.47054
Kang, Kyungkeun; Perthame, Benoit; Stevens, Angela; Velázquez, J. J. L.
2009
Asymmetric potentials and motor effect: a homogenization approach. Zbl 1180.35081
Perthame, Benoît; Souganidis, Panagiotis E.
2009
Asymmetric potentials and motor effect: a large deviation approach. Zbl 1171.82012
Perthame, Benoît; Souganidis, Panagiotis E.
2009
Why hyperbolic and kinetic models for cell populations self-organization? Zbl 1197.35297
Perthame, Benoît
2009
Dirac concentrations in Lotka-Volterra parabolic PDEs. Zbl 1172.35005
Perthame, Benoit; Barles, Guy
2008
Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces. Zbl 1134.92006
Corrias, Lucilla; Perthame, Benoît
2008
Traveling waves for the Keller-Segel system with Fisher birth terms. Zbl 1154.35459
Nadin, Gregoire; Perthame, Benoît; Ryzhik, Lenya
2008
An age-and-cyclin-structured cell population model for healthy and tumoral tissues. Zbl 1148.92014
Brikci, Fadia Bekkal; Clairambault, Jean; Ribba, Benjamin; Perthame, Benoît
2008
Energy concentration and Sommerfeld condition for Helmholtz equation with variable index at infinity. Zbl 1137.35020
Perthame, Benoit; Vega, Luis
2008
Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Zbl 1134.92012
Brikci, Fadia Bekkal; Clairambault, Jean; Perthame, Benoît
2008
Global existence for a kinetic model of chemotaxis via dispersion and Strichartz estimates. Zbl 1137.92004
Bournaveas, Nikolaos; Calvez, Vincent; Gutiérrez, Susana; Perthame, Benoît
2008
Mathematical methods and modeling of biophysical phenomena. Zbl 1155.92302
Perthame, Benoit; Markowich, Peter; Zubelli, Jorge P.
2008
Analysis of a cell system with finite divisions. Zbl 1244.35153
Perthame, Benôıt; Touaoula, Tarik Mohamed
2008
Transport equations in biology. Zbl 1185.92006
Perthame, Benoît
2007
Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Zbl 1337.35077
Perthame, Benoît; Génieys, Stephane
2007
Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. Zbl 1137.49027
Barles, Guy; Perthame, Benoît
2007
On the inverse problem for a size-structured population model. Zbl 1118.35072
Perthame, Benoît; Zubelli, Jorge P.
2007
Upwinding of the source term at interfaces for Euler equations with high friction. Zbl 1213.76123
Bouchut, Francois; Ounaissa, Haythem; Perthame, Benoît
2007
Modified Keller-Segel system and critical mass for the log interaction kernel. Zbl 1126.35077
Calvez, Vincent; Perthame, Benoît; Sharifi tabar, Mohsen
2007
Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model. Zbl 1106.92053
2007
...and 136 more Documents
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#### Cited by 3,604 Authors

 126 Perthame, Benoît 52 Carrillo de la Plata, José Antonio 31 Jabin, Pierre-Emmanuel 30 Bouchut, François 30 Shu, Chi-Wang 29 Zhang, Xianwen 28 Jin, Shi 27 Bellomo, Nicola 27 Calvez, Vincent 25 Kurganov, Alexander 25 Laurençot, Philippe 24 Berthon, Christophe 24 Chen, Gui-Qiang G. 24 Vauchelet, Nicolas 23 Winkler, Michael 22 Degond, Pierre 22 Fernández-Nieto, Enrique Domingo 22 Karlsen, Kenneth Hvistendahl 22 Liu, Jianguo 22 Souganidis, Panagiotis E. 21 Goudon, Thierry 21 Mischler, Stéphane 21 Pareschi, Lorenzo 21 Yang, Tong 19 Golse, François 19 Lorenzi, Tommaso 19 Lu, Yunguang 19 Markowich, Peter Alexander 19 Parés Madroñal, Carlos 19 Rein, Gerhard 18 Gosse, Laurent 18 Gwiazda, Piotr 18 Hérard, Jean-Marc 18 Yun, Seok-Bae 17 Barles, Guy 17 Bellouquid, Abdelghani 17 Chalons, Christophe 17 Lions, Pierre-Louis 17 Mai Duc Thanh 17 Natalini, Roberto 16 Filbet, Francis 16 Mirrahimi, Sepideh 15 Desvillettes, Laurent 15 Doumic, Marie 15 Ducomet, Bernard 15 Gess, Benjamin 15 Masmoudi, Nader 15 Mieussens, Luc 15 Saint-Raymond, Laure 15 Soler, Juan S. 15 Volpert, Vitaly A. 14 Andreianov, Boris 14 Coquel, Frédéric 14 Escobedo Martínez, Miguel 14 Martínez Gamba, Irene 14 Nečasová, Šárka 14 Schaeffer, Jack W. 14 Velázquez, Juan J. L. 14 Wang, Zhian 14 Xing, Yulong 13 Castro, Manuel J. 13 Chertock, Alina E. 13 Ha, Seung-Yeal 13 Huang, Feimin 13 Raoul, Gaël 13 Schmeiser, Christian 13 Zhang, Xiangxiong 12 Audusse, Emmanuel 12 Bouin, Emeric 12 Bresch, Didier 12 Gabriel, Pierre 12 Lemou, Mohammed 12 Liu, Hailiang 12 Lorz, Alexander 12 Popov, Boyan 12 Risebro, Nils Henrik 12 Tadmor, Eitan 11 Biler, Piotr 11 Chen, Zili 11 Clairambault, Jean 11 Dimarco, Giacomo 11 Hwang, Hyung Ju 11 Jüngel, Ansgar 11 Klar, Axel 11 LeFloch, Philippe Gerard 11 Lian, Ruxu 11 Mangeney, Anne 11 Puppo, Gabriella 11 Rendall, Alan D. 11 Tao, Youshan 11 Trofimchuk, Sergei I. 11 Vega, Luis 11 Zheng, Jiashan 10 Bisi, Marzia 10 Bourdarias, Christian 10 Bristeau, Marie-Odile 10 Delitala, Marcello 10 Dumbser, Michael 10 Fox, Rodney O. 10 Godlewski, Edwige ...and 3,504 more Authors
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#### Cited in 322 Serials

 228 Journal of Computational Physics 191 Journal of Differential Equations 139 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 115 Journal of Mathematical Analysis and Applications 97 Communications in Partial Differential Equations 95 Archive for Rational Mechanics and Analysis 76 Journal of Mathematical Biology 71 Computers and Fluids 69 Journal of Scientific Computing 63 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 62 SIAM Journal on Mathematical Analysis 62 Kinetic and Related Models 60 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 60 Comptes Rendus. Mathématique. Académie des Sciences, Paris 56 Journal de Mathématiques Pures et Appliquées. Neuvième Série 55 Journal of Statistical Physics 53 Communications in Mathematical Physics 47 Mathematics of Computation 47 Journal of Functional Analysis 44 Discrete and Continuous Dynamical Systems 41 Applied Mathematics Letters 40 Nonlinear Analysis. Real World Applications 39 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 38 Journal of Mathematical Physics 38 Mathematical Methods in the Applied Sciences 38 Journal of Hyperbolic Differential Equations 37 Discrete and Continuous Dynamical Systems. Series B 36 Mathematical and Computer Modelling 32 Numerische Mathematik 30 Computers & Mathematics with Applications 30 Transport Theory and Statistical Physics 30 Acta Applicandae Mathematicae 30 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 29 ZAMP. Zeitschrift für angewandte Mathematik und Physik 29 Transactions of the American Mathematical Society 27 SIAM Journal on Numerical Analysis 27 European Journal of Mechanics. B. Fluids 26 Nonlinearity 26 Bulletin of Mathematical Biology 24 Applied Mathematics and Computation 24 Journal of Theoretical Biology 23 Physica D 22 SIAM Journal on Scientific Computing 21 Communications on Pure and Applied Mathematics 21 Quarterly of Applied Mathematics 20 Journal of Fluid Mechanics 20 NoDEA. Nonlinear Differential Equations and Applications 19 Computer Methods in Applied Mechanics and Engineering 19 Journal of Computational and Applied Mathematics 19 Networks and Heterogeneous Media 18 Applied Mathematics and Optimization 18 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 17 International Journal for Numerical Methods in Fluids 17 Chinese Annals of Mathematics. Series B 17 Calculus of Variations and Partial Differential Equations 16 Mathematical Biosciences 16 SIAM Journal on Applied Mathematics 16 Journal of Evolution Equations 15 Physics of Fluids 15 Multiscale Modeling & Simulation 14 Applied Mathematical Modelling 14 Mathematical Biosciences and Engineering 14 Nonlinear Analysis. Theory, Methods & Applications 13 Mathematical Modelling of Natural Phenomena 13 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 12 Applied Numerical Mathematics 12 Journal of Biological Dynamics 11 Proceedings of the American Mathematical Society 11 Stochastic Processes and their Applications 10 Applicable Analysis 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 9 European Journal of Applied Mathematics 9 The Annals of Applied Probability 9 Journal of Nonlinear Science 9 Continuum Mechanics and Thermodynamics 9 Communications on Pure and Applied Analysis 8 Advances in Mathematics 8 Japan Journal of Industrial and Applied Mathematics 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 8 Bulletin of the American Mathematical Society. New Series 8 Journal of Dynamics and Differential Equations 8 Analysis and Applications (Singapore) 8 Boundary Value Problems 8 Séminaire Laurent Schwartz. EDP et Applications 7 Journal of Engineering Mathematics 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 The Annals of Probability 7 Mathematische Annalen 7 Monatshefte für Mathematik 7 Revista Matemática Iberoamericana 7 Numerical Methods for Partial Differential Equations 7 Journal of Mathematical Sciences (New York) 7 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 7 Abstract and Applied Analysis 7 Journal of Mathematical Fluid Mechanics 7 Bulletin of the Brazilian Mathematical Society. New Series 7 Stochastic and Partial Differential Equations. Analysis and Computations 7 SMAI Journal of Computational Mathematics 6 Journal of Optimization Theory and Applications 6 Ricerche di Matematica ...and 222 more Serials
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#### Cited in 48 Fields

 2,469 Partial differential equations (35-XX) 1,205 Fluid mechanics (76-XX) 908 Biology and other natural sciences (92-XX) 750 Numerical analysis (65-XX) 634 Statistical mechanics, structure of matter (82-XX) 220 Probability theory and stochastic processes (60-XX) 192 Integral equations (45-XX) 183 Calculus of variations and optimal control; optimization (49-XX) 119 Ordinary differential equations (34-XX) 107 Operator theory (47-XX) 79 Dynamical systems and ergodic theory (37-XX) 79 Geophysics (86-XX) 65 Systems theory; control (93-XX) 64 Optics, electromagnetic theory (78-XX) 62 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 61 Astronomy and astrophysics (85-XX) 57 Mechanics of deformable solids (74-XX) 50 Classical thermodynamics, heat transfer (80-XX) 37 Operations research, mathematical programming (90-XX) 34 Relativity and gravitational theory (83-XX) 33 Functional analysis (46-XX) 33 Quantum theory (81-XX) 30 Mechanics of particles and systems (70-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 21 Global analysis, analysis on manifolds (58-XX) 19 Statistics (62-XX) 16 Differential geometry (53-XX) 15 Real functions (26-XX) 10 Computer science (68-XX) 7 General and overarching topics; collections (00-XX) 6 Measure and integration (28-XX) 6 Integral transforms, operational calculus (44-XX) 5 Combinatorics (05-XX) 5 Approximations and expansions (41-XX) 5 Information and communication theory, circuits (94-XX) 4 Functions of a complex variable (30-XX) 3 History and biography (01-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 General topology (54-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Mathematics education (97-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1

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