Edit Profile (opens in new tab) Métivier, Guy Compute Distance To: Compute Author ID: metivier.guy Published as: Métivier, Guy; Métivier, G.; Metivier, Guy; Metivier, G. Homepage: https://www.math.u-bordeaux.fr/~gmetivie/ External Links: MGP · Wikidata · ResearchGate · GND · IdRef · theses.fr Documents Indexed: 156 Publications since 1973, including 5 Books 1 Contribution as Editor Co-Authors: 34 Co-Authors with 104 Joint Publications 728 Co-Co-Authors all top 5 Co-Authors 53 single-authored 42 Rauch, Jeffrey B. 36 Joly, Jean-Luc 18 Zumbrun, Kevin R. 11 Guès, Olivier 10 Williams, Mark 7 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 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 1 Texier, Benjamin 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 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 155 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 114 Publications have been cited 1,447 times in 938 Documents Cited by ▼ Year ▼ The incompressible limit of the non-isentropic Euler equations. Zbl 0974.76072Métivier, G.; Schochet, S. 101 2001 Stability of multidimensional shocks. Zbl 1017.35075Métivier, Guy 48 2001 Para-differential calculus and applications to the Cauchy problem for nonlinear systems. Zbl 1156.35002Métivier, Guy 43 2008 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066Métivier, Guy; Zumbrun, Kevin 42 2005 Coherent and focusing multidimensional nonlinear geometric optics. Zbl 0836.35087Joly, J.-L.; Métivier, G.; Rauch, J. 41 1995 The block structure condition for symmetric hyperbolic systems. Zbl 1073.35525Métivier, Guy 40 2000 Fonction spectrale et valeurs propres d’une classe d’opérateurs non elliptiques. Zbl 0376.35012Metivier, Guy 37 1976 Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Zbl 0815.35066Joly, J.-L.; Metivier, G.; Rauch, J. 37 1993 Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155Métivier, Guy; Zumbrun, Kevin 35 2005 Analytic hypoellipticity for operators with multiple characteristics. Zbl 0455.35040Metivier, Guy 35 1981 Valeurs propres d’opérateurs définis par la restriction de systèmes variationnels à des sous-espaces. Zbl 0328.35029Métivier, Guy 35 1978 Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Zbl 1207.35082Alazard, Thomas; Métivier, Guy 32 2009 Propagation de l’analyticité des solutions de systèmes hyperboliques non-linéaires. Zbl 0545.35063Alinhac, S.; Métivier, G. 30 1984 Une classe d’opérateurs non hypoelliptiques analytiques. Zbl 0455.35041Metivier, Guy 30 1980 Resonant one dimensional nonlinear geometric optics. Zbl 0851.35023Joly, J.-L.; Métivier, G.; Rauch, J. 30 1993 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 0619.35075Métivier, Guy 29 1986 Recent mathematical results and open problems about shallow water equations. Zbl 1291.35001Bresch, Didier; Desjardins, Benoît; Métivier, Guy 28 2007 Hypoellipticite analytique sur des groupes nilpotents de rang 2. Zbl 0433.35015Metivier, Guy 28 1980 Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 27 2005 Averaging theorems for conservative systems and the weakly compressible Euler equations. Zbl 1029.34035Métivier, G.; Schochet, S. 26 2003 Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 25 2006 Global solutions to Maxwell equations in a ferromagnetic medium. Zbl 0964.35155Joly, J. L.; Métivier, G.; Rauch, J. 23 2000 Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Zbl 1217.35136Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 22 2010 Diffractive nonlinear geometric optics with rectification. Zbl 0928.35093Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 22 1998 Valeurs propres de problèmes aux limites elliptiques irréguliers. Zbl 0401.35088Metivier, Guy 20 1977 Focusing at a point and absorption of nonlinear oscillations. Zbl 0857.35087Joly, J. L.; Métivier, G.; Rauch, J. 19 1995 Existence of weak shocks for multidimenional quasilinear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0996.35001Francheteau, Jacques; Métivier, Guy 18 2000 Propriété des iterés et ellipticite. Zbl 0388.35063Metivier, Guy 18 1978 Transparent nonlinear geometric optics and Maxwell-Bloch equations. Zbl 1170.78311Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 17 2000 Coherent nonlinear waves and the Wiener algebra. Zbl 0791.35019Joly, J.-L.; Métivier, G.; Rauch, J. 17 1994 Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2005 The Cauchy problem for semilinear hyperbolic systems with discontinuous data. Zbl 0631.35056Metivier, Guy 16 1986 Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations. Zbl 1099.35094Bresch, Didier; Métivier, Guy 14 2006 Remarks on the well-posedness of the nonlinear Cauchy problem. Zbl 1071.35074Métivier, Guy 14 2005 The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations. Zbl 1172.35041Colombini, Ferruccio; Métivier, Guy 13 2008 Théorie spectrale des opérateurs uniformement elliptiques sur quelques ouverts irréguliers. Zbl 0251.35074Fleckinger, Jacqueline; Metivier, Guy 13 1973 Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 13 2004 Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients. Zbl 1286.35057Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 11 2013 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 0606.76027Alinhac, S.; Métivier, G. 11 1986 Stability of multidimensional weak shocks. Zbl 0711.35078Métivier, Guy 11 1990 Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 10 2008 A nonlinear instability for \(3\times 3\) systems of conservation laws. Zbl 0820.35093Joly, J. L.; Metivier, G.; Rauch, J. 10 1994 Diffractive nonlinear geometric optics. Zbl 0910.35076Donnat, P.; Joly, J.-L.; Métivier, G.; Rauch, J. 10 1996 Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332Métivier, G.; Zumbrun, K. 10 2004 Small viscosity and boundary layer methods. Theory, stability analysis, and applications. Zbl 1133.35001Métivier, Guy 9 2004 Analytic vectors of hypoelliptic operators of principal type. Zbl 0496.35026Baouendi, M. S.; Metivier, G. 9 1982 Ondes soniques. (Sonic waves). Zbl 0728.35068Métivier, G. 9 1991 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 0608.35026Bolley, P.; Camus, J.; Metivier, G. 9 1986 Progressing wave solutions to certain nonlinear mixed problems. Zbl 0613.35050Beals, Michael; Metivier, Guy 9 1986 Instabilities in Zakharov equations for laser propagation in a plasma. Zbl 1133.35303Colin, Thierry; Métivier, Guy 8 2006 A well-posedness result for hyperbolic operators with Zygmund coefficients. Zbl 1282.35220Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 8 2013 Spectral asymptotics for the delta-Neumann problem. Zbl 0489.35064Metivier, Guy 8 1981 Propagation, interaction and reflection of discontinuous progressing waves for semilinear hyperbolic systems. Zbl 0687.35021Metivier, Guy 8 1989 Reflection of transversal progressing waves in nonlinear strictly hyperbolic mixed problems. Zbl 0633.35051Beals, Michael; Métivier, Guy 8 1987 Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems. Zbl 1133.35404Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 7 2007 The mathematics of nonlinear optics. Zbl 1191.35263Métivier, Guy 7 2009 Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) Zbl 1091.35039Cheverry, Christophe; Guès, Olivier; Métivier, Guy 7 2003 Trilinear resonant interactions of semilinear hyperbolic waves. Zbl 0955.35007Métivier, G.; Schochet, S. 7 1998 Nonlinear oscillations beyond caustics. Zbl 0862.35066Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 7 1996 Global solvability of the anharmonic oscillator model from nonlinear optics. Zbl 0859.35124Joly, J. L.; Metivier, G.; Rauch, J. 7 1996 Nonlinear high frequency hyperbolic waves. Zbl 0824.35077Joly, J. L.; Metivier, G.; Rauch, J. 7 1992 Uniqueness and approximation of solutions of first order nonlinear equations. Zbl 0594.35018Metivier, Guy 7 1985 Non-hypoellipticite analytique pour D//\(x^ 2\) + (\(x^ 2\) + \(y^ 2)\) D//\(y^ 2\). Zbl 0481.35033Metivier, Guy 7 1981 Remarques sur l’optique géométrique non linéaire multidimensionnelle. (Remarks on nonlinear multidimensional geometric optics). Zbl 0749.35055Joly, J. L.; Metivier, G.; Rauch, J. 7 1991 The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients. Zbl 1346.35124Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 7 2015 Nonlinear hyperbolic smoothing at a focal point. Zbl 0989.35093Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 7 2000 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1187.35136Métivier, Guy; Zumbrun, Kevin 7 2003 Anelastic limits for Euler-type systems. Zbl 1204.35117Bresch, Didier; Métivier, Guy 6 2010 Counterexamples to Hölmgren’s uniqueness for analytic nonlinear Cauchy problems. Zbl 0794.35026Métivier, G. 6 1993 Kernels and symbols of analytic pseudodifferential operators. Zbl 0535.35081Baouendi, M. S.; Goulaouic, C.; Métivier, G. 6 1983 \(L^2\) 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 1332.35205Métivier, Guy 6 2014 Boundary layer and long time stability for multidimensional viscous shocks. Zbl 1108.35115Guès, O.; Métivier, G.; Williams, M.; Zumbrun, K. 6 2004 Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Zbl 1197.76116Métivier, Guy; Zumbrun, K. 5 2009 Caustics for dissipative semilinear oscillations. Zbl 0963.35114Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 5 2000 Hypberbolic domains of determinacy and Hamilton-Jacobi equations. Zbl 1090.35114Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 5 2005 Trilinear compensated compactness and nonlinear geometric optics. Zbl 0840.35013Joly, J. L.; Métivier, G.; Rauch, J. 5 1995 Electromagnetic wave propagation in presence of a ferromagnetic material. (Propagation des ondes électromagnétiques en présence d’un matériau ferromagnétique.) Zbl 0913.65119Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 5 1998 Propagation de l’analyticité des solutions d’équations non- linéaires de type principal. Zbl 0566.35017Alinhac, S.; Metivier, G. 5 1984 Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations. Zbl 0711.35080Métivier, Guy; Rauch, Jeffrey 5 1990 Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels. (Nonlinear problems and stability of multidimensional shocks). Zbl 0659.35063Métivier, Guy 5 1987 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 1406.35490Lannes, David; Métivier, Guy 5 2018 Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems. Zbl 1316.35172Colombini, Ferruccio; Métivier, Guy 4 2015 Nonlinear geometric optics and Maxwell-Bloch equations. (Optique géométrique non linéaire et équations de Maxwell-Bloch.) Zbl 1086.35526Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 4 1999 Rigorous resonant 1-d nonlinear geometric optics. Zbl 0718.35094Joly, J. L.; Métivier, G.; Rauch, J. 4 1990 Existence of semilinear relaxation shocks. Zbl 1180.35358Métivier, Guy; Zumbrun, Kevin 4 2009 Large-amplitude high-frequency waves for quasilinear hyperbolic systems. Zbl 1107.35079Cheverry, C.; Guès, O.; Métivier, G. 3 2004 Dispersive stabilization. Zbl 1192.35165Métivier, Guy; Rauch, Jeffrey 3 2010 Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 3 2008 Incompressible limit of nonisentropic Euler equations. (Limite incompressible des équations d’Euler non isentropiques.) Zbl 1061.76074Métivier, Guy; Schochet, Steven 3 2001 Several recent results in nonlinear geometric optics. Zbl 0854.35115Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1996 The existence of weak shocks for multidimensional quasi-linear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0918.35092Francheteau, Jacques; Métivier, Guy 3 1998 Recent results in nonlinear geometric optics. Zbl 0938.35034Métivier, Guy; Joly, Jean-Luc; Rauch, Jeffrey 3 1999 Caustics for dissipative semilinear oscillations. Zbl 0891.35098Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1997 Théorie spectrale d’opérateurs elliptiques sur des ouverts irréguliers. Zbl 0264.47040Metivier, G. 3 1973 Comportement asymptotique des valeurs propres d’opérateurs elliptiques dégénérées. Zbl 0329.35047Metivier, Guy 3 1976 On the \(L^2\) well posedness of hyperbolic initial boundary value problems. (Sur le problème mixte hyperbolique dans \(L^2\).) Zbl 1437.35461Métivier, Guy 3 2017 Problemes de Cauchy et ondes non linéaires. Zbl 0606.35051Metivier, Guy 2 1986 Strictly dissipative nonuniqueness with corners. Zbl 1377.35193Métivier, Guy; Rauch, Jeffrey 2 2017 Existence of quasilinear relaxation shock profiles in systems with characteristic velocities. Zbl 1278.34027Métivier, Guy; Texier, Benjamin; Zumbrun, Kevin 1 2012 Estimation du reste en théorie spectrale. Zbl 0542.35055Métivier, Guy 1 1983 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 1406.35490Lannes, David; Métivier, Guy 5 2018 Note on strongly hyperbolic systems with involutive characteristics. Zbl 1415.35180Métivier, 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 1437.35461Métivier, Guy 3 2017 Strictly dissipative nonuniqueness with corners. Zbl 1377.35193Métivier, Guy; Rauch, Jeffrey 2 2017 The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients. Zbl 1346.35124Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 7 2015 Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems. Zbl 1316.35172Colombini, Ferruccio; Métivier, Guy 4 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 1332.35205Métivier, 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 1295.35035Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 1 2014 A note on complete hyperbolic operators with log-Zygmund coefficients. Zbl 1320.35179Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 1 2014 Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients. Zbl 1286.35057Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 11 2013 A well-posedness result for hyperbolic operators with Zygmund coefficients. Zbl 1282.35220Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 8 2013 Existence of quasilinear relaxation shock profiles in systems with characteristic velocities. Zbl 1278.34027Métivier, Guy; Texier, Benjamin; Zumbrun, Kevin 1 2012 Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Zbl 1217.35136Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 22 2010 Anelastic limits for Euler-type systems. Zbl 1204.35117Bresch, Didier; Métivier, Guy 6 2010 Dispersive stabilization. Zbl 1192.35165Métivier, Guy; Rauch, Jeffrey 3 2010 Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Zbl 1207.35082Alazard, Thomas; Métivier, Guy 32 2009 The mathematics of nonlinear optics. Zbl 1191.35263Métivier, Guy 7 2009 Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Zbl 1197.76116Métivier, Guy; Zumbrun, K. 5 2009 Existence of semilinear relaxation shocks. Zbl 1180.35358Métivier, Guy; Zumbrun, Kevin 4 2009 Para-differential calculus and applications to the Cauchy problem for nonlinear systems. Zbl 1156.35002Métivier, Guy 43 2008 The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations. Zbl 1172.35041Colombini, Ferruccio; Métivier, Guy 13 2008 Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 10 2008 Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 3 2008 Recent mathematical results and open problems about shallow water equations. Zbl 1291.35001Bresch, Didier; Desjardins, Benoît; Métivier, Guy 28 2007 Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems. Zbl 1133.35404Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 7 2007 Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 25 2006 Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations. Zbl 1099.35094Bresch, Didier; Métivier, Guy 14 2006 Instabilities in Zakharov equations for laser propagation in a plasma. Zbl 1133.35303Colin, Thierry; Métivier, Guy 8 2006 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066Métivier, Guy; Zumbrun, Kevin 42 2005 Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155Métivier, Guy; Zumbrun, Kevin 35 2005 Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 27 2005 Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2005 Remarks on the well-posedness of the nonlinear Cauchy problem. Zbl 1071.35074Métivier, Guy 14 2005 Hypberbolic domains of determinacy and Hamilton-Jacobi equations. Zbl 1090.35114Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 5 2005 Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 13 2004 Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332Métivier, G.; Zumbrun, K. 10 2004 Small viscosity and boundary layer methods. Theory, stability analysis, and applications. Zbl 1133.35001Métivier, Guy 9 2004 Boundary layer and long time stability for multidimensional viscous shocks. Zbl 1108.35115Guès, O.; Métivier, G.; Williams, M.; Zumbrun, K. 6 2004 Large-amplitude high-frequency waves for quasilinear hyperbolic systems. Zbl 1107.35079Cheverry, C.; Guès, O.; Métivier, G. 3 2004 Averaging theorems for conservative systems and the weakly compressible Euler equations. Zbl 1029.34035Métivier, G.; Schochet, S. 26 2003 Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) Zbl 1091.35039Cheverry, Christophe; Guès, Olivier; Métivier, Guy 7 2003 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1187.35136Métivier, Guy; Zumbrun, Kevin 7 2003 The incompressible limit of the non-isentropic Euler equations. Zbl 0974.76072Métivier, G.; Schochet, S. 101 2001 Stability of multidimensional shocks. Zbl 1017.35075Métivier, Guy 48 2001 Incompressible limit of nonisentropic Euler equations. (Limite incompressible des équations d’Euler non isentropiques.) Zbl 1061.76074Métivier, Guy; Schochet, Steven 3 2001 The block structure condition for symmetric hyperbolic systems. Zbl 1073.35525Métivier, Guy 40 2000 Global solutions to Maxwell equations in a ferromagnetic medium. Zbl 0964.35155Joly, J. L.; Métivier, G.; Rauch, J. 23 2000 Existence of weak shocks for multidimenional quasilinear hyperbolic systems. (Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels.) Zbl 0996.35001Francheteau, Jacques; Métivier, Guy 18 2000 Transparent nonlinear geometric optics and Maxwell-Bloch equations. Zbl 1170.78311Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 17 2000 Nonlinear hyperbolic smoothing at a focal point. Zbl 0989.35093Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 7 2000 Caustics for dissipative semilinear oscillations. Zbl 0963.35114Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 5 2000 Nonlinear geometric optics and Maxwell-Bloch equations. (Optique géométrique non linéaire et équations de Maxwell-Bloch.) Zbl 1086.35526Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 4 1999 Recent results in nonlinear geometric optics. Zbl 0938.35034Métivier, Guy; Joly, Jean-Luc; Rauch, Jeffrey 3 1999 Diffractive nonlinear geometric optics with rectification. Zbl 0928.35093Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 22 1998 Trilinear resonant interactions of semilinear hyperbolic waves. Zbl 0955.35007Métivier, 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 0913.65119Joly, 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 0918.35092Francheteau, Jacques; Métivier, Guy 3 1998 Dense oscillations for the compressible 2D Euler equations. Zbl 0952.35102Joly, J. L.; Metivier, G.; Rauch, J. 1 1998 Caustics for dissipative semilinear oscillations. Zbl 0891.35098Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1997 Diffractive nonlinear geometric optics. Zbl 0910.35076Donnat, P.; Joly, J.-L.; Métivier, G.; Rauch, J. 10 1996 Nonlinear oscillations beyond caustics. Zbl 0862.35066Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 7 1996 Global solvability of the anharmonic oscillator model from nonlinear optics. Zbl 0859.35124Joly, J. L.; Metivier, G.; Rauch, J. 7 1996 Several recent results in nonlinear geometric optics. Zbl 0854.35115Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1996 Dense oscillations for the Euler equations. II. Zbl 0920.35112Joly, J.-L.; Metivier, G.; Rauch, J. 1 1996 Coherent and focusing multidimensional nonlinear geometric optics. Zbl 0836.35087Joly, J.-L.; Métivier, G.; Rauch, J. 41 1995 Focusing at a point and absorption of nonlinear oscillations. Zbl 0857.35087Joly, J. L.; Métivier, G.; Rauch, J. 19 1995 Trilinear compensated compactness and nonlinear geometric optics. Zbl 0840.35013Joly, J. L.; Métivier, G.; Rauch, J. 5 1995 Coherent nonlinear waves and the Wiener algebra. Zbl 0791.35019Joly, J.-L.; Métivier, G.; Rauch, J. 17 1994 A nonlinear instability for \(3\times 3\) systems of conservation laws. Zbl 0820.35093Joly, J. L.; Metivier, G.; Rauch, J. 10 1994 Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Zbl 0815.35066Joly, J.-L.; Metivier, G.; Rauch, J. 37 1993 Resonant one dimensional nonlinear geometric optics. Zbl 0851.35023Joly, J.-L.; Métivier, G.; Rauch, J. 30 1993 Counterexamples to Hölmgren’s uniqueness for analytic nonlinear Cauchy problems. Zbl 0794.35026Métivier, G. 6 1993 Focusing and absorption of nonlinear oscillations. Zbl 0815.35071Joly, J. L.; Métivier, G.; Rauch, J. 1 1993 Nonlinear high frequency hyperbolic waves. Zbl 0824.35077Joly, J. L.; Metivier, G.; Rauch, J. 7 1992 Ondes soniques. (Sonic waves). Zbl 0728.35068Métivier, G. 9 1991 Remarques sur l’optique géométrique non linéaire multidimensionnelle. (Remarks on nonlinear multidimensional geometric optics). Zbl 0749.35055Joly, J. L.; Metivier, G.; Rauch, J. 7 1991 Vecteurs analytiques réduits et analyticité. (Reduced analytic vectors and analyticity). Zbl 0735.35043Bolley, Pierre; Camus, Jacques; Metivier, Guy 1 1991 Stability of multidimensional weak shocks. Zbl 0711.35078Métivier, Guy 11 1990 Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations. Zbl 0711.35080Métivier, Guy; Rauch, Jeffrey 5 1990 Rigorous resonant 1-d nonlinear geometric optics. Zbl 0718.35094Joly, J. L.; Métivier, G.; Rauch, J. 4 1990 Propagation, interaction and reflection of discontinuous progressing waves for semilinear hyperbolic systems. Zbl 0687.35021Metivier, Guy 8 1989 The interaction of two progressing waves. Zbl 0697.35093Métivier, Guy; Rauch, Jeffrey 1 1989 Reflection of transversal progressing waves in nonlinear strictly hyperbolic mixed problems. Zbl 0633.35051Beals, Michael; Métivier, Guy 8 1987 Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels. (Nonlinear problems and stability of multidimensional shocks). Zbl 0659.35063Métivier, Guy 5 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 0619.35075Métivier, Guy 29 1986 The Cauchy problem for semilinear hyperbolic systems with discontinuous data. Zbl 0631.35056Metivier, 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 0606.76027Alinhac, S.; Métivier, G. 11 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 0608.35026Bolley, P.; Camus, J.; Metivier, G. 9 1986 Progressing wave solutions to certain nonlinear mixed problems. Zbl 0613.35050Beals, Michael; Metivier, Guy 9 1986 Problemes de Cauchy et ondes non linéaires. Zbl 0606.35051Metivier, Guy 2 1986 Uniqueness and approximation of solutions of first order nonlinear equations. Zbl 0594.35018Metivier, Guy 7 1985 Propagation de l’analyticité des solutions de systèmes hyperboliques non-linéaires. Zbl 0545.35063Alinhac, S.; Métivier, G. 30 1984 Propagation de l’analyticité des solutions d’équations non- linéaires de type principal. Zbl 0566.35017Alinhac, S.; Metivier, G. 5 1984 Kernels and symbols of analytic pseudodifferential operators. Zbl 0535.35081Baouendi, M. S.; Goulaouic, C.; Métivier, G. 6 1983 Estimation du reste en théorie spectrale. Zbl 0542.35055Métivier, Guy 1 1983 Estimation du reste en théorie spectrale. Zbl 0558.35050Metivier, Guy 1 1983 Analytic vectors of hypoelliptic operators of principal type. Zbl 0496.35026Baouendi, M. S.; Metivier, G. 9 1982 Non hypoellipticite analytique pour des opérateurs à caractéristiques doubles. Zbl 0489.35033Metivier, G. 1 1982 Analytic hypoellipticity for operators with multiple characteristics. Zbl 0455.35040Metivier, Guy 35 1981 Spectral asymptotics for the delta-Neumann problem. Zbl 0489.35064Metivier, Guy 8 1981 ...and 14 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 876 Authors 48 Zumbrun, Kevin R. 39 Métivier, Guy 28 Rauch, Jeffrey B. 16 Alazard, Thomas 16 Williams, Mark 15 Guès, Olivier 14 Himonas, A. Alexandrou 14 Trakhinin, Yuri L. 14 Wang, Ya-Guang 13 Cheverry, Christophe 12 Fan, Jishan 11 Bove, Antonio 11 Carles, Rémi 11 Chen, Shuxing 11 Coulombel, Jean-François 11 Fanelli, Francesco 11 Tartakoff, David S. 10 Chen, Gui-Qiang G. 10 Derridj, Makhlouf 10 Li, Fucai 10 Petronilho, Gerson 9 Chen, Hua 9 Colin, Thierry 9 Del Santo, Daniele 9 Li, Dening 8 Lannes, David 8 Schochet, Steven H. 8 Temam, Roger Meyer 7 Freistühler, Heinrich 7 Joly, Jean-Luc 7 Rousset, Frédéric 7 Texier, Benjamin 7 Wang, Yaguang 7 Xin, Zhouping 7 Yin, Huicheng 6 Barker, Blake 6 Benoit, Antoine 6 Bresch, Didier 6 Colombini, Ferruccio 6 Cordaro, Paulo D. 6 Godin, Paul 6 Hanges, Nicholas William 6 Humpherys, Jeffrey 6 Jiang, Song 6 Ju, Qiangchang 6 Lapidus, Michel L. 6 Morando, Alessandro 6 Nakamura, Gen 6 Nguyen, Huy Quang 6 Nguyen, Toan Trong 6 Rothschild, Linda Preiss 6 Sueur, Franck 6 Trebeschi, Paola 6 Wang, Tao 6 Zhu, Shengguo 5 Benzoni-Gavage, Sylvie 5 Christ, Michael 5 Gallagher, Isabelle 5 Helffer, Bernard 5 Junca, Stéphane 5 Li, Jingna 5 Lyng, Gregory Daniel 5 Masmoudi, Nader 5 Montalto, Riccardo 5 Mughetti, Marco 5 Ou, Yaobin 5 Trélat, Emmanuel 5 Wang, Dehua 5 Xie, Chunjing 5 Zhang, Ping 5 Zhou, Yong 4 Alinhac, Serge 4 Audiard, Corentin 4 Baldi, Pietro 4 Barsukow, Wasilij 4 Berti, Massimiliano 4 Burq, Nicolas 4 Cheng, Bin 4 Chinni, Gregorio 4 Cimrák, Ivan 4 Desjardins, Benoît 4 Duchêne, Vincent 4 Dumas, Éric 4 Feireisl, Eduard 4 Fleckinger, Jacqueline 4 Gallice, Gérard 4 Grenier, Emmanuel 4 Guerra, Graziano 4 Kopachevskiĭ, Nikolaĭ Dmitrievich 4 Li, Yeping 4 Macías-Díaz, Jorge Eduardo 4 Nkonga, Boniface 4 Paicu, Marius 4 Pausader, Benoît 4 Plaza, Ramón G. 4 Secchi, Paolo 4 Slodička, Marián 4 Tang, Tong 4 Xiang, Wei 4 Yang, Zhao ...and 776 more Authors all top 5 Cited in 196 Serials 84 Journal of Differential Equations 64 Communications in Partial Differential Equations 63 Archive for Rational Mechanics and Analysis 22 Transactions of the American Mathematical Society 20 Communications in Mathematical Physics 20 Journal of Functional Analysis 20 Journal de Mathématiques Pures et Appliquées. Neuvième Série 19 Duke Mathematical Journal 19 Journal of Hyperbolic Differential Equations 18 Journal of Mathematical Analysis and Applications 18 Physica D 17 Proceedings of the American Mathematical Society 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Annales de l’Institut Fourier 15 SIAM Journal on Mathematical Analysis 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Advances in Mathematics 12 Journal of Mathematical Fluid Mechanics 11 Quarterly of Applied Mathematics 10 Journal of Mathematical Physics 10 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Communications on Pure and Applied Mathematics 9 Mathematische Annalen 9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Journal of Computational Physics 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 8 Kinetic and Related Models 7 Memoirs of the American Mathematical Society 7 Calculus of Variations and Partial Differential Equations 7 Discrete and Continuous Dynamical Systems 7 Communications on Pure and Applied Analysis 6 Nonlinearity 6 Zeitschrift für Analysis und ihre Anwendungen 6 Applied Mathematics Letters 6 Science China. Mathematics 6 Séminaire Laurent Schwartz. EDP et Applications 5 Mathematical Methods in the Applied Sciences 5 Mathematics of Computation 5 Inventiones Mathematicae 5 Mathematische Zeitschrift 5 Communications in Contemporary Mathematics 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Nonlinear Analysis. Theory, Methods & Applications 4 Journal of Computational and Applied Mathematics 4 Proceedings of the Japan Academy. Series A 4 Chinese Annals of Mathematics. Series B 4 Acta Applicandae Mathematicae 4 Asymptotic Analysis 4 Acta Mathematica Sinica. New Series 4 Abstract and Applied Analysis 4 Wuhan University Journal of Natural Sciences (WUJNS) 4 Nonlinear Analysis. Real World Applications 4 Journal of Evolution Equations 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Pseudo-Differential Operators and Applications 4 Complex Analysis and its Synergies 4 Annals of PDE 4 Water Waves 3 Computers and Fluids 3 Computers & Mathematics with Applications 3 Journal d’Analyse Mathématique 3 Monatshefte für Mathematik 3 Numerische Mathematik 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Siberian Mathematical Journal 3 Applied Numerical Mathematics 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Journal of the American Mathematical Society 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Dynamics and Differential Equations 3 Journal of Nonlinear Science 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Journal of Mathematical Sciences (New York) 3 Journal of the Institute of Mathematics of Jussieu 3 Discrete and Continuous Dynamical Systems. Series S 2 Israel Journal of Mathematics 2 Arkiv för Matematik 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Computation 2 Bulletin de la Société Mathématique de France 2 Journal of the Mathematical Society of Japan 2 Journal of Soviet Mathematics 2 Mathematische Nachrichten 2 Osaka Journal of Mathematics 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matematico della Università di Padova 2 SIAM Journal on Numerical Analysis 2 Acta Mathematicae Applicatae Sinica. English Series 2 Revista Matemática Iberoamericana 2 Science in China. Series A 2 The Journal of Geometric Analysis 2 Applications of Mathematics 2 Stochastic Processes and their Applications 2 Bulletin of the American Mathematical Society. New Series 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 NoDEA. Nonlinear Differential Equations and Applications 2 Bulletin des Sciences Mathématiques 2 Integral Transforms and Special Functions ...and 96 more Serials all top 5 Cited in 43 Fields 840 Partial differential equations (35-XX) 368 Fluid mechanics (76-XX) 68 Optics, electromagnetic theory (78-XX) 43 Global analysis, analysis on manifolds (58-XX) 42 Numerical analysis (65-XX) 35 Statistical mechanics, structure of matter (82-XX) 32 Operator theory (47-XX) 26 Mechanics of deformable solids (74-XX) 24 Differential geometry (53-XX) 22 Dynamical systems and ergodic theory (37-XX) 21 Topological groups, Lie groups (22-XX) 19 Several complex variables and analytic spaces (32-XX) 19 Ordinary differential equations (34-XX) 17 Functional analysis (46-XX) 16 Classical thermodynamics, heat transfer (80-XX) 16 Quantum theory (81-XX) 16 Geophysics (86-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 11 Abstract harmonic analysis (43-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Probability theory and stochastic processes (60-XX) 9 Real functions (26-XX) 8 Systems theory; control (93-XX) 5 Nonassociative rings and algebras (17-XX) 5 Functions of a complex variable (30-XX) 5 Relativity and gravitational theory (83-XX) 4 Measure and integration (28-XX) 4 Mechanics of particles and systems (70-XX) 4 Astronomy and astrophysics (85-XX) 3 Number theory (11-XX) 3 Biology and other natural sciences (92-XX) 2 Potential theory (31-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-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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