Edit Profile (opens in new tab) Métivier, Guy Co-Author Distance Author ID: metivier.guy Published as: Métivier, Guy; Métivier, G.; Metivier, Guy; Metivier, G. more...less Homepage: https://www.math.u-bordeaux.fr/~gmetivie/ External Links: MGP · Wikidata · ResearchGate · GND · IdRef · theses.fr Documents Indexed: 159 Publications since 1973, including 5 Books and 2 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 34 Co-Authors with 107 Joint Publications 811 Co-Co-Authors all top 5 Co-Authors 53 single-authored 42 Rauch, Jeffrey B. 36 Joly, Jean-Luc 20 Zumbrun, Kevin R. 11 Guès, Olivier 10 Williams, Mark 8 Colombini, Ferruccio 6 Alinhac, Serge 6 Camus, Jacques 5 Bolley, Pierre 5 Del Santo, Daniele 5 Fanelli, Francesco 5 Schochet, Steven H. 4 Bresch, Didier 3 Baouendi, Mohammed Salah 2 Beals, Michael 2 Cheverry, Christophe 2 Francheteau, Jacques 2 Lannes, David 2 Texier, Benjamin 1 Alazard, Thomas 1 Berthé, Valérie 1 Besse, Philippe C. 1 Colin, Thierry 1 Dehornoy, Patrick 1 Desjardins, Benoît 1 Donnat, Phillipe 1 Fleckinger, Jacqueline 1 Goulaouic, Charles 1 Guès, C. M. I. Olivier 1 Lebœuf, Patricio 1 Massot, Marc 1 Nishitani, Tatsuo 1 Patras, Frédéric 1 Sentis, Remi all top 5 Serials 13 Séminaire Équations aux Dérivées Partielles 12 Communications in Partial Differential Equations 7 Duke Mathematical Journal 6 Journal of Differential Equations 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Archive for Rational Mechanics and Analysis 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 American Journal of Mathematics 3 Indiana University Mathematics Journal 3 Inventiones Mathematicae 2 Communications in Mathematical Physics 2 Communications on Pure and Applied Mathematics 2 Annales de l’Institut Fourier 2 Bulletin of the London Mathematical Society 2 Journal of Functional Analysis 2 Memoirs of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Analysis & PDE 2 Journal de l’École Polytechnique – Mathématiques 1 Nonlinearity 1 Michigan Mathematical Journal 1 Physica D 1 Journal of the American Mathematical Society 1 Differential and Integral Equations 1 SIAM Journal on Mathematical Analysis 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Advances in Differential Equations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Annals of Mathematics. Second Series 1 Annales Henri Poincaré 1 Acta Mathematica Scientia. Series B. (English Edition) 1 AMRX. Applied Mathematics Research eXpress 1 Journal of Hyperbolic Differential Equations 1 Bulletin de la Société Mathématique de France. Supplément. Mémoires 1 Astérisque 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Matapli 1 Kyoto Journal of Mathematics 1 Modeling and Simulation in Science, Engineering and Technology 1 Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) all top 5 Fields 157 Partial differential equations (35-XX) 30 Optics, electromagnetic theory (78-XX) 29 Fluid mechanics (76-XX) 5 Operator theory (47-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 118 Publications have been cited 1,741 times in 1,130 Documents Cited by ▼ Year ▼ The incompressible limit of the non-isentropic Euler equations. Zbl 0974.76072 Métivier, G.; Schochet, S. 137 2001 Para-differential calculus and applications to the Cauchy problem for nonlinear systems. Zbl 1156.35002 Métivier, Guy 75 2008 Stability of multidimensional shocks. Zbl 1017.35075 Métivier, Guy 70 2001 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066 Métivier, Guy; Zumbrun, Kevin 51 2005 Coherent and focusing multidimensional nonlinear geometric optics. Zbl 0836.35087 Joly, J.-L.; Métivier, G.; Rauch, J. 46 1995 The block structure condition for symmetric hyperbolic systems. Zbl 1073.35525 Métivier, Guy 44 2000 Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Zbl 1207.35082 Alazard, Thomas; Métivier, Guy 42 2009 Fonction spectrale et valeurs propres d’une classe d’opérateurs non elliptiques. Zbl 0376.35012 Metivier, Guy 42 1976 Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Zbl 0815.35066 Joly, J.-L.; Metivier, G.; Rauch, J. 42 1993 Recent mathematical results and open problems about shallow water equations. Zbl 1291.35001 Bresch, Didier; Desjardins, Benoît; Métivier, Guy 39 2007 Valeurs propres d’opérateurs définis par la restriction de systèmes variationnels à des sous-espaces. Zbl 0328.35029 Métivier, Guy 38 1978 Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155 Métivier, Guy; Zumbrun, Kevin 37 2005 Analytic hypoellipticity for operators with multiple characteristics. Zbl 0455.35040 Metivier, Guy 36 1981 Averaging theorems for conservative systems and the weakly compressible Euler equations. Zbl 1029.34035 Métivier, G.; Schochet, S. 35 2003 Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082 Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 33 2006 Une classe d’opérateurs non hypoelliptiques analytiques. Zbl 0455.35041 Metivier, Guy 33 1980 Propagation de l’analyticité des solutions de systèmes hyperboliques non-linéaires. Zbl 0545.35063 Alinhac, S.; Métivier, G. 32 1984 Hypoellipticite analytique sur des groupes nilpotents de rang 2. Zbl 0433.35015 Metivier, Guy 31 1980 Resonant one dimensional nonlinear geometric optics. Zbl 0851.35023 Joly, J.-L.; Métivier, G.; Rauch, J. 31 1993 Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 30 2005 Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d’espace. (Interaction of two shock waves for a system with two conservation laws in two dimensional space). Zbl 0619.35075 Métivier, Guy 29 1986 Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Zbl 1217.35136 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 26 2010 Global solutions to Maxwell equations in a ferromagnetic medium. Zbl 0964.35155 Joly, J. L.; Métivier, G.; Rauch, J. 25 2000 Diffractive nonlinear geometric optics with rectification. Zbl 0928.35093 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 24 1998 Existence of weak shocks for multidimenional quasilinear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0996.35001 Francheteau, Jacques; Métivier, Guy 22 2000 Transparent nonlinear geometric optics and Maxwell-Bloch equations. Zbl 1170.78311 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 22 2000 Remarks on the well-posedness of the nonlinear Cauchy problem. Zbl 1071.35074 Métivier, Guy 22 2005 Propriété des iterés et ellipticite. Zbl 0388.35063 Metivier, Guy 22 1978 Valeurs propres de problèmes aux limites elliptiques irréguliers. Zbl 0401.35088 Metivier, Guy 22 1977 Focusing at a point and absorption of nonlinear oscillations. Zbl 0857.35087 Joly, J. L.; Métivier, G.; Rauch, J. 21 1995 Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations. Zbl 1099.35094 Bresch, Didier; Métivier, Guy 19 2006 Coherent nonlinear waves and the Wiener algebra. Zbl 0791.35019 Joly, J.-L.; Métivier, G.; Rauch, J. 17 1994 The Cauchy problem for semilinear hyperbolic systems with discontinuous data. Zbl 0631.35056 Metivier, Guy 16 1986 Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2004 The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations. Zbl 1172.35041 Colombini, Ferruccio; Métivier, Guy 16 2008 Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2005 Small viscosity and boundary layer methods. Theory, stability analysis, and applications. Zbl 1133.35001 Métivier, Guy 15 2004 Stability of multidimensional weak shocks. Zbl 0711.35078 Métivier, Guy 15 1990 Analytic vectors of hypoelliptic operators of principal type. Zbl 0496.35026 Baouendi, M. S.; Metivier, G. 14 1982 Théorie spectrale des opérateurs uniformement elliptiques sur quelques ouverts irréguliers. Zbl 0251.35074 Fleckinger, Jacqueline; Metivier, Guy 13 1973 Non-hypoellipticite analytique pour \(D_x^2 + (x^2 + y^2) D_y^2\). Zbl 0481.35033 Metivier, Guy 12 1981 The mathematics of nonlinear optics. Zbl 1191.35263 Métivier, Guy 12 2009 Propagation de l’analyticité locale pour les solutions de l’équation d’Euler. (Propagation of local analyticity for the solutions of the Euler equation). Zbl 0606.76027 Alinhac, S.; Métivier, G. 12 1986 Diffractive nonlinear geometric optics. Zbl 0910.35076 Donnat, P.; Joly, J.-L.; Métivier, G.; Rauch, J. 12 1996 Estimations de Schauder et régularité Höldérienne pour une classe de problèmes aux limites singuliers. (Schauder estimates and Hölder regularity for a class of singular boundary value problems). Zbl 0608.35026 Bolley, P.; Camus, J.; Metivier, G. 11 1986 Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052 Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 11 2008 Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients. Zbl 1286.35057 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 11 2013 Instabilities in Zakharov equations for laser propagation in a plasma. Zbl 1133.35303 Colin, Thierry; Métivier, Guy 10 2006 Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332 Métivier, G.; Zumbrun, K. 10 2004 Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) Zbl 1091.35039 Cheverry, Christophe; Guès, Olivier; Métivier, Guy 10 2003 A nonlinear instability for \(3\times 3\) systems of conservation laws. Zbl 0820.35093 Joly, J. L.; Metivier, G.; Rauch, J. 10 1994 Progressing wave solutions to certain nonlinear mixed problems. Zbl 0613.35050 Beals, Michael; Metivier, Guy 9 1986 Ondes soniques. (Sonic waves). Zbl 0728.35068 Métivier, G. 9 1991 The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients. Zbl 1346.35124 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 9 2015 The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations. (Le problème du rivage pour les équations de Saint-Venant et de Green-Naghdi uni-dimensionnelles.) Zbl 1406.35490 Lannes, David; Métivier, Guy 9 2018 Reflection of transversal progressing waves in nonlinear strictly hyperbolic mixed problems. Zbl 0633.35051 Beals, Michael; Métivier, Guy 8 1987 Spectral asymptotics for the delta-Neumann problem. Zbl 0489.35064 Metivier, Guy 8 1981 Kernels and symbols of analytic pseudodifferential operators. Zbl 0535.35081 Baouendi, M. S.; Goulaouic, C.; Métivier, G. 8 1983 Propagation, interaction and reflection of discontinuous progressing waves for semilinear hyperbolic systems. Zbl 0687.35021 Metivier, Guy 8 1989 Nonlinear oscillations beyond caustics. Zbl 0862.35066 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 8 1996 Global solvability of the anharmonic oscillator model from nonlinear optics. Zbl 0859.35124 Joly, J. L.; Metivier, G.; Rauch, J. 8 1996 A well-posedness result for hyperbolic operators with Zygmund coefficients. Zbl 1282.35220 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 8 2013 Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems. Zbl 1133.35404 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 7 2007 Trilinear resonant interactions of semilinear hyperbolic waves. Zbl 0955.35007 Métivier, G.; Schochet, S. 7 1998 Nonlinear hyperbolic smoothing at a focal point. Zbl 0989.35093 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 7 2000 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1187.35136 Métivier, Guy; Zumbrun, Kevin 7 2003 Uniqueness and approximation of solutions of first order nonlinear equations. Zbl 0594.35018 Metivier, Guy 7 1985 Remarques sur l’optique géométrique non linéaire multidimensionnelle. (Remarks on nonlinear multidimensional geometric optics). Zbl 0749.35055 Joly, J. L.; Metivier, G.; Rauch, J. 7 1991 Counterexamples to Hölmgren’s uniqueness for analytic nonlinear Cauchy problems. Zbl 0794.35026 Métivier, G. 7 1993 Nonlinear high frequency hyperbolic waves. Zbl 0824.35077 Joly, J. L.; Metivier, G.; Rauch, J. 7 1992 Anelastic limits for Euler-type systems. Zbl 1204.35117 Bresch, Didier; Métivier, Guy 7 2010 Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels. (Nonlinear problems and stability of multidimensional shocks). Zbl 0659.35063 Métivier, Guy 6 1987 Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Zbl 1197.76116 Métivier, Guy; Zumbrun, K. 6 2009 Caustics for dissipative semilinear oscillations. Zbl 0963.35114 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 6 2000 Trilinear compensated compactness and nonlinear geometric optics. Zbl 0840.35013 Joly, J. L.; Métivier, G.; Rauch, J. 6 1995 Boundary layer and long time stability for multidimensional viscous shocks. Zbl 1108.35115 Guès, O.; Métivier, G.; Williams, M.; Zumbrun, K. 6 2004 Hypberbolic domains of determinacy and Hamilton-Jacobi equations. Zbl 1090.35114 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 6 2005 Rigorous resonant 1-d nonlinear geometric optics. Zbl 0718.35094 Joly, J. L.; Métivier, G.; Rauch, J. 6 1990 \(L^2\) well-posed Cauchy problems and symmetrizability of first order systems. (Problèmes de Cauchy bien posés dans \(L^2\) et symétrisabilité pour les systèmes du premier ordre.) Zbl 1332.35205 Métivier, Guy 6 2014 Dispersive stabilization. Zbl 1192.35165 Métivier, Guy; Rauch, Jeffrey 5 2010 Propagation de l’analyticité des solutions d’équations non- linéaires de type principal. Zbl 0566.35017 Alinhac, S.; Metivier, G. 5 1984 Electromagnetic wave propagation in presence of a ferromagnetic material. (Propagation des ondes électromagnétiques en présence d’un matériau ferromagnétique.) Zbl 0913.65119 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 5 1998 Large-amplitude high-frequency waves for quasilinear hyperbolic systems. Zbl 1107.35079 Cheverry, C.; Guès, O.; Métivier, G. 5 2004 Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations. Zbl 0711.35080 Métivier, Guy; Rauch, Jeffrey 5 1990 Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems. Zbl 1316.35172 Colombini, Ferruccio; Métivier, Guy 5 2015 Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 4 2008 Several recent results in nonlinear geometric optics. Zbl 0854.35115 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 4 1996 Recent results in nonlinear geometric optics. Zbl 0938.35034 Métivier, Guy; Joly, Jean-Luc; Rauch, Jeffrey 4 1999 Existence of semilinear relaxation shocks. Zbl 1180.35358 Métivier, Guy; Zumbrun, Kevin 4 2009 Comportement asymptotique des valeurs propres d’opérateurs elliptiques dégénérées. Zbl 0329.35047 Metivier, Guy 4 1976 Nonlinear geometric optics and Maxwell-Bloch equations. (Optique géométrique non linéaire et équations de Maxwell-Bloch.) Zbl 1086.35526 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 4 1999 Waves interacting with a partially immersed obstacle in the Boussinesq regime. Zbl 07413798 Bresch, Didier; Lannes, David; Métivier, Guy 4 2021 On the \(L^2\) well posedness of hyperbolic initial boundary value problems. (Sur le problème mixte hyperbolique dans \(L^2\).) Zbl 1437.35461 Métivier, Guy 4 2017 The existence of weak shocks for multidimensional quasi-linear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0918.35092 Francheteau, Jacques; Métivier, Guy 3 1998 Théorie spectrale d’opérateurs elliptiques sur des ouverts irréguliers. Zbl 0264.47040 Metivier, G. 3 1973 Incompressible limit of nonisentropic Euler equations. (Limite incompressible des équations d’Euler non isentropiques.) Zbl 1061.76074 Métivier, Guy; Schochet, Steven 3 2001 Caustics for dissipative semilinear oscillations. Zbl 0891.35098 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1997 Strictly dissipative nonuniqueness with corners. Zbl 1377.35193 Métivier, Guy; Rauch, Jeffrey 3 2017 Dense oscillations for the compressible 2D Euler equations. Zbl 0952.35102 Joly, J. L.; Metivier, G.; Rauch, J. 2 1998 Problemes de Cauchy et ondes non linéaires. Zbl 0606.35051 Metivier, Guy 2 1986 Waves interacting with a partially immersed obstacle in the Boussinesq regime. Zbl 07413798 Bresch, Didier; Lannes, David; Métivier, Guy 4 2021 On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients. Zbl 1439.35317 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 1 2020 The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations. (Le problème du rivage pour les équations de Saint-Venant et de Green-Naghdi uni-dimensionnelles.) Zbl 1406.35490 Lannes, David; Métivier, Guy 9 2018 Note on strongly hyperbolic systems with involutive characteristics. Zbl 1415.35180 Métivier, Guy; Nishitani, Tatsuo 1 2018 On the \(L^2\) well posedness of hyperbolic initial boundary value problems. (Sur le problème mixte hyperbolique dans \(L^2\).) Zbl 1437.35461 Métivier, Guy 4 2017 Strictly dissipative nonuniqueness with corners. Zbl 1377.35193 Métivier, Guy; Rauch, Jeffrey 3 2017 The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients. Zbl 1346.35124 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 9 2015 Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems. Zbl 1316.35172 Colombini, Ferruccio; Métivier, Guy 5 2015 \(L^2\) well-posed Cauchy problems and symmetrizability of first order systems. (Problèmes de Cauchy bien posés dans \(L^2\) et symétrisabilité pour les systèmes du premier ordre.) Zbl 1332.35205 Métivier, Guy 6 2014 Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions. (Couches limites visqueuses pour des systèmes hyperboliques-paraboliques avec condition aux limites de Neumann.) Zbl 1295.35035 Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 1 2014 A note on complete hyperbolic operators with log-Zygmund coefficients. Zbl 1320.35179 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 1 2014 Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients. Zbl 1286.35057 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 11 2013 A well-posedness result for hyperbolic operators with Zygmund coefficients. Zbl 1282.35220 Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 8 2013 Existence of quasilinear relaxation shock profiles in systems with characteristic velocities. Zbl 1278.34027 Métivier, Guy; Texier, Benjamin; Zumbrun, Kevin 1 2012 Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Zbl 1217.35136 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 26 2010 Anelastic limits for Euler-type systems. Zbl 1204.35117 Bresch, Didier; Métivier, Guy 7 2010 Dispersive stabilization. Zbl 1192.35165 Métivier, Guy; Rauch, Jeffrey 5 2010 Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Zbl 1207.35082 Alazard, Thomas; Métivier, Guy 42 2009 The mathematics of nonlinear optics. Zbl 1191.35263 Métivier, Guy 12 2009 Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Zbl 1197.76116 Métivier, Guy; Zumbrun, K. 6 2009 Existence of semilinear relaxation shocks. Zbl 1180.35358 Métivier, Guy; Zumbrun, Kevin 4 2009 Para-differential calculus and applications to the Cauchy problem for nonlinear systems. Zbl 1156.35002 Métivier, Guy 75 2008 The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations. Zbl 1172.35041 Colombini, Ferruccio; Métivier, Guy 16 2008 Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052 Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 11 2008 Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 4 2008 Recent mathematical results and open problems about shallow water equations. Zbl 1291.35001 Bresch, Didier; Desjardins, Benoît; Métivier, Guy 39 2007 Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems. Zbl 1133.35404 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 7 2007 Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082 Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 33 2006 Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations. Zbl 1099.35094 Bresch, Didier; Métivier, Guy 19 2006 Instabilities in Zakharov equations for laser propagation in a plasma. Zbl 1133.35303 Colin, Thierry; Métivier, Guy 10 2006 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066 Métivier, Guy; Zumbrun, Kevin 51 2005 Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155 Métivier, Guy; Zumbrun, Kevin 37 2005 Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 30 2005 Remarks on the well-posedness of the nonlinear Cauchy problem. Zbl 1071.35074 Métivier, Guy 22 2005 Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2005 Hypberbolic domains of determinacy and Hamilton-Jacobi equations. Zbl 1090.35114 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 6 2005 Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162 Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2004 Small viscosity and boundary layer methods. Theory, stability analysis, and applications. Zbl 1133.35001 Métivier, Guy 15 2004 Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332 Métivier, G.; Zumbrun, K. 10 2004 Boundary layer and long time stability for multidimensional viscous shocks. Zbl 1108.35115 Guès, O.; Métivier, G.; Williams, M.; Zumbrun, K. 6 2004 Large-amplitude high-frequency waves for quasilinear hyperbolic systems. Zbl 1107.35079 Cheverry, C.; Guès, O.; Métivier, G. 5 2004 Averaging theorems for conservative systems and the weakly compressible Euler equations. Zbl 1029.34035 Métivier, G.; Schochet, S. 35 2003 Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) Zbl 1091.35039 Cheverry, Christophe; Guès, Olivier; Métivier, Guy 10 2003 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1187.35136 Métivier, Guy; Zumbrun, Kevin 7 2003 The incompressible limit of the non-isentropic Euler equations. Zbl 0974.76072 Métivier, G.; Schochet, S. 137 2001 Stability of multidimensional shocks. Zbl 1017.35075 Métivier, Guy 70 2001 Incompressible limit of nonisentropic Euler equations. (Limite incompressible des équations d’Euler non isentropiques.) Zbl 1061.76074 Métivier, Guy; Schochet, Steven 3 2001 The block structure condition for symmetric hyperbolic systems. Zbl 1073.35525 Métivier, Guy 44 2000 Global solutions to Maxwell equations in a ferromagnetic medium. Zbl 0964.35155 Joly, J. L.; Métivier, G.; Rauch, J. 25 2000 Existence of weak shocks for multidimenional quasilinear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0996.35001 Francheteau, Jacques; Métivier, Guy 22 2000 Transparent nonlinear geometric optics and Maxwell-Bloch equations. Zbl 1170.78311 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 22 2000 Nonlinear hyperbolic smoothing at a focal point. Zbl 0989.35093 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 7 2000 Caustics for dissipative semilinear oscillations. Zbl 0963.35114 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 6 2000 Recent results in nonlinear geometric optics. Zbl 0938.35034 Métivier, Guy; Joly, Jean-Luc; Rauch, Jeffrey 4 1999 Nonlinear geometric optics and Maxwell-Bloch equations. (Optique géométrique non linéaire et équations de Maxwell-Bloch.) Zbl 1086.35526 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 4 1999 Diffractive nonlinear geometric optics with rectification. Zbl 0928.35093 Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 24 1998 Trilinear resonant interactions of semilinear hyperbolic waves. Zbl 0955.35007 Métivier, G.; Schochet, S. 7 1998 Electromagnetic wave propagation in presence of a ferromagnetic material. (Propagation des ondes électromagnétiques en présence d’un matériau ferromagnétique.) Zbl 0913.65119 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 5 1998 The existence of weak shocks for multidimensional quasi-linear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0918.35092 Francheteau, Jacques; Métivier, Guy 3 1998 Dense oscillations for the compressible 2D Euler equations. Zbl 0952.35102 Joly, J. L.; Metivier, G.; Rauch, J. 2 1998 Caustics for dissipative semilinear oscillations. Zbl 0891.35098 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1997 Diffractive nonlinear geometric optics. Zbl 0910.35076 Donnat, P.; Joly, J.-L.; Métivier, G.; Rauch, J. 12 1996 Nonlinear oscillations beyond caustics. Zbl 0862.35066 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 8 1996 Global solvability of the anharmonic oscillator model from nonlinear optics. Zbl 0859.35124 Joly, J. L.; Metivier, G.; Rauch, J. 8 1996 Several recent results in nonlinear geometric optics. Zbl 0854.35115 Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 4 1996 Dense oscillations for the Euler equations. II. Zbl 0920.35112 Joly, J.-L.; Metivier, G.; Rauch, J. 1 1996 Coherent and focusing multidimensional nonlinear geometric optics. Zbl 0836.35087 Joly, J.-L.; Métivier, G.; Rauch, J. 46 1995 Focusing at a point and absorption of nonlinear oscillations. Zbl 0857.35087 Joly, J. L.; Métivier, G.; Rauch, J. 21 1995 Trilinear compensated compactness and nonlinear geometric optics. Zbl 0840.35013 Joly, J. L.; Métivier, G.; Rauch, J. 6 1995 Coherent nonlinear waves and the Wiener algebra. Zbl 0791.35019 Joly, J.-L.; Métivier, G.; Rauch, J. 17 1994 A nonlinear instability for \(3\times 3\) systems of conservation laws. Zbl 0820.35093 Joly, J. L.; Metivier, G.; Rauch, J. 10 1994 Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Zbl 0815.35066 Joly, J.-L.; Metivier, G.; Rauch, J. 42 1993 Resonant one dimensional nonlinear geometric optics. Zbl 0851.35023 Joly, J.-L.; Métivier, G.; Rauch, J. 31 1993 Counterexamples to Hölmgren’s uniqueness for analytic nonlinear Cauchy problems. Zbl 0794.35026 Métivier, G. 7 1993 Focusing and absorption of nonlinear oscillations. Zbl 0815.35071 Joly, J. L.; Métivier, G.; Rauch, J. 1 1993 Nonlinear high frequency hyperbolic waves. Zbl 0824.35077 Joly, J. L.; Metivier, G.; Rauch, J. 7 1992 Ondes soniques. (Sonic waves). Zbl 0728.35068 Métivier, G. 9 1991 Remarques sur l’optique géométrique non linéaire multidimensionnelle. (Remarks on nonlinear multidimensional geometric optics). Zbl 0749.35055 Joly, J. L.; Metivier, G.; Rauch, J. 7 1991 Vecteurs analytiques réduits et analyticité. (Reduced analytic vectors and analyticity). Zbl 0735.35043 Bolley, Pierre; Camus, Jacques; Metivier, Guy 1 1991 Stability of multidimensional weak shocks. Zbl 0711.35078 Métivier, Guy 15 1990 Rigorous resonant 1-d nonlinear geometric optics. Zbl 0718.35094 Joly, J. L.; Métivier, G.; Rauch, J. 6 1990 Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations. Zbl 0711.35080 Métivier, Guy; Rauch, Jeffrey 5 1990 Théorème d’unicité pour des vecteurs analytiques. (Uniqueness theorem for analytic vectors). Zbl 0704.35031 Bolley, Pierre; Camus, Jacques; Métivier, Guy 2 1990 Propagation, interaction and reflection of discontinuous progressing waves for semilinear hyperbolic systems. Zbl 0687.35021 Metivier, Guy 8 1989 The interaction of two progressing waves. Zbl 0697.35093 Métivier, Guy; Rauch, Jeffrey 1 1989 Reflection of transversal progressing waves in nonlinear strictly hyperbolic mixed problems. Zbl 0633.35051 Beals, Michael; Métivier, Guy 8 1987 Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels. (Nonlinear problems and stability of multidimensional shocks). Zbl 0659.35063 Métivier, Guy 6 1987 Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d’espace. (Interaction of two shock waves for a system with two conservation laws in two dimensional space). Zbl 0619.35075 Métivier, Guy 29 1986 The Cauchy problem for semilinear hyperbolic systems with discontinuous data. Zbl 0631.35056 Metivier, Guy 16 1986 Propagation de l’analyticité locale pour les solutions de l’équation d’Euler. (Propagation of local analyticity for the solutions of the Euler equation). Zbl 0606.76027 Alinhac, S.; Métivier, G. 12 1986 Estimations de Schauder et régularité Höldérienne pour une classe de problèmes aux limites singuliers. (Schauder estimates and Hölder regularity for a class of singular boundary value problems). Zbl 0608.35026 Bolley, P.; Camus, J.; Metivier, G. 11 1986 Progressing wave solutions to certain nonlinear mixed problems. Zbl 0613.35050 Beals, Michael; Metivier, Guy 9 1986 Problemes de Cauchy et ondes non linéaires. Zbl 0606.35051 Metivier, Guy 2 1986 Uniqueness and approximation of solutions of first order nonlinear equations. Zbl 0594.35018 Metivier, Guy 7 1985 Propagation de l’analyticité des solutions de systèmes hyperboliques non-linéaires. Zbl 0545.35063 Alinhac, S.; Métivier, G. 32 1984 Propagation de l’analyticité des solutions d’équations non- linéaires de type principal. Zbl 0566.35017 Alinhac, S.; Metivier, G. 5 1984 Kernels and symbols of analytic pseudodifferential operators. Zbl 0535.35081 Baouendi, M. S.; Goulaouic, C.; Métivier, G. 8 1983 Estimation du reste en théorie spectrale. Zbl 0542.35055 Métivier, Guy 1 1983 Estimation du reste en théorie spectrale. Zbl 0558.35050 Metivier, Guy 1 1983 Analytic vectors of hypoelliptic operators of principal type. Zbl 0496.35026 Baouendi, M. S.; Metivier, G. 14 1982 ...and 18 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,053 Authors 51 Zumbrun, Kevin R. 42 Métivier, Guy 28 Rauch, Jeffrey B. 19 Alazard, Thomas 18 Fan, Jishan 18 Trakhinin, Yuri L. 17 Williams, Mark 16 Cheverry, Christophe 16 Guès, Olivier 15 Li, Fucai 14 Chen, Hua 14 Himonas, A. Alexandrou 14 Wang, Ya-Guang 13 Carles, Rémi 13 Fanelli, Francesco 12 Chen, Gui-Qiang G. 12 Coulombel, Jean-François 12 Derridj, Makhlouf 12 Zhu, Shengguo 11 Bove, Antonio 11 Chen, Shuxing 11 Ju, Qiangchang 11 Tartakoff, David S. 10 Del Santo, Daniele 10 Lannes, David 10 Petronilho, Gerson 10 Schochet, Steven H. 9 Bresch, Didier 9 Colin, Thierry 9 Li, Dening 9 Morando, Alessandro 9 Nakamura, Gen 9 Rousset, Frédéric 9 Secchi, Paolo 9 Texier, Benjamin 9 Trebeschi, Paola 8 Benoit, Antoine 8 Chinni, Gregorio 8 Ou, Yaobin 8 Temam, Roger Meyer 8 Wang, Tao 8 Xin, Zhouping 8 Zhang, Zhifei 7 Berti, Massimiliano 7 Colombini, Ferruccio 7 Freistühler, Heinrich 7 Joly, Jean-Luc 7 Masmoudi, Nader 7 Nguyen, Huy Quang 7 Nguyen, Toan Trong 7 Tang, Tong 7 Wang, Dehua 7 Wang, Yaguang 7 Xie, Chunjing 7 Yin, Huicheng 7 Zhou, Yong 6 Barker, Blake 6 Burq, Nicolas 6 Chen, Hongge 6 Cordaro, Paulo D. 6 Feola, Roberto 6 Godin, Paul 6 Hanges, Nicholas William 6 Humpherys, Jeffrey 6 Jiang, Song 6 Lapidus, Michel L. 6 Montalto, Riccardo 6 Mughetti, Marco 6 Rothschild, Linda Preiss 6 Sueur, Franck 6 Xiang, Wei 5 Audiard, Corentin 5 Baldi, Pietro 5 Barsukow, Wasilij 5 Benzoni-Gavage, Sylvie 5 Chen, Robin Ming 5 Christ, Michael 5 Desjardins, Benoît 5 Duchêne, Vincent 5 Helffer, Bernard 5 Huang, Feimin 5 Ifrim, Mihaela 5 Junca, Stéphane 5 Li, Jingna 5 Lyng, Gregory Daniel 5 Pusateri, Fabio 5 Strani, Marta 5 Tataru, Daniel 5 Trélat, Emmanuel 5 Yuan, Difan 5 Zhang, Ping 5 Zuily, Claude 4 Albano, Paolo 4 Alinhac, Serge 4 Babin, Anatoli V. 4 Cheng, Bin 4 Cicognani, Massimo 4 Cimrák, Ivan 4 Dumas, Éric 4 Fang, Beixiang ...and 953 more Authors all top 5 Cited in 222 Serials 96 Journal of Differential Equations 70 Archive for Rational Mechanics and Analysis 66 Communications in Partial Differential Equations 30 SIAM Journal on Mathematical Analysis 26 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Transactions of the American Mathematical Society 22 Communications in Mathematical Physics 22 Journal of Functional Analysis 19 Duke Mathematical Journal 19 Physica D 19 Journal of Hyperbolic Differential Equations 18 Journal of Mathematical Analysis and Applications 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 17 Proceedings of the American Mathematical Society 17 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 15 Annales de l’Institut Fourier 14 Mathematische Annalen 14 Quarterly of Applied Mathematics 14 Journal of Mathematical Fluid Mechanics 13 Journal of Mathematical Physics 12 Advances in Mathematics 11 Communications on Pure and Applied Mathematics 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Calculus of Variations and Partial Differential Equations 11 Discrete and Continuous Dynamical Systems 10 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Memoirs of the American Mathematical Society 9 Communications on Pure and Applied Analysis 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Kinetic and Related Models 8 Journal of Computational Physics 8 Mathematical Methods in the Applied Sciences 8 Nonlinearity 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 8 Applied Mathematics Letters 8 Journal of Nonlinear Science 8 Nonlinear Analysis. Real World Applications 7 Mathematische Zeitschrift 7 Zeitschrift für Analysis und ihre Anwendungen 7 Journal of Pseudo-Differential Operators and Applications 7 Annals of PDE 6 Inventiones Mathematicae 6 Journal of Dynamics and Differential Equations 6 Communications in Contemporary Mathematics 6 Journal of Evolution Equations 6 Discrete and Continuous Dynamical Systems. Series B 6 Science China. Mathematics 6 Séminaire Laurent Schwartz. EDP et Applications 5 Mathematics of Computation 5 Acta Applicandae Mathematicae 5 Asymptotic Analysis 5 Acta Mathematica Scientia. Series B. (English Edition) 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Discrete and Continuous Dynamical Systems. Series S 5 Analysis & PDE 5 Complex Analysis and its Synergies 5 Nonlinear Analysis. Theory, Methods & Applications 4 Israel Journal of Mathematics 4 Bulletin de la Société Mathématique de France 4 Journal of Computational and Applied Mathematics 4 Monatshefte für Mathematik 4 Proceedings of the Japan Academy. Series A 4 Chinese Annals of Mathematics. Series B 4 Acta Mathematica Sinica. New Series 4 Abstract and Applied Analysis 4 Wuhan University Journal of Natural Sciences (WUJNS) 4 Water Waves 3 Computers and Fluids 3 Computers & Mathematics with Applications 3 Journal d’Analyse Mathématique 3 Mathematische Nachrichten 3 Numerische Mathematik 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 SIAM Journal on Numerical Analysis 3 Siberian Mathematical Journal 3 Applied Numerical Mathematics 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Journal of the American Mathematical Society 3 Journal of Scientific Computing 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Bulletin of the American Mathematical Society. New Series 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Journal of Mathematical Sciences (New York) 3 NoDEA. Nonlinear Differential Equations and Applications 3 Acta Mathematica Sinica. English Series 3 Annales Henri Poincaré 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Journal of the Institute of Mathematics of Jussieu 3 Annales Henri Lebesgue 2 Journal of Fluid Mechanics 2 Letters in Mathematical Physics 2 Arkiv för Matematik 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Computation 2 Indiana University Mathematics Journal 2 Integral Equations and Operator Theory 2 Journal of the Mathematical Society of Japan 2 Journal of Soviet Mathematics 2 Osaka Journal of Mathematics ...and 122 more Serials all top 5 Cited in 46 Fields 1,024 Partial differential equations (35-XX) 482 Fluid mechanics (76-XX) 71 Optics, electromagnetic theory (78-XX) 50 Global analysis, analysis on manifolds (58-XX) 48 Numerical analysis (65-XX) 42 Operator theory (47-XX) 41 Statistical mechanics, structure of matter (82-XX) 34 Mechanics of deformable solids (74-XX) 28 Dynamical systems and ergodic theory (37-XX) 26 Differential geometry (53-XX) 22 Topological groups, Lie groups (22-XX) 22 Ordinary differential equations (34-XX) 21 Functional analysis (46-XX) 21 Quantum theory (81-XX) 21 Geophysics (86-XX) 20 Several complex variables and analytic spaces (32-XX) 19 Classical thermodynamics, heat transfer (80-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 15 Real functions (26-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 12 Abstract harmonic analysis (43-XX) 12 Probability theory and stochastic processes (60-XX) 11 Systems theory; control (93-XX) 8 Measure and integration (28-XX) 7 Relativity and gravitational theory (83-XX) 6 Mechanics of particles and systems (70-XX) 6 Astronomy and astrophysics (85-XX) 5 Nonassociative rings and algebras (17-XX) 5 Functions of a complex variable (30-XX) 4 Biology and other natural sciences (92-XX) 3 Number theory (11-XX) 2 Potential theory (31-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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