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: 157 Publications since 1973, including 5 Books 1 Contribution as Editor Co-Authors: 34 Co-Authors with 105 Joint Publications 759 Co-Co-Authors all top 5 Co-Authors 53 single-authored 42 Rauch, Jeffrey B. 36 Joly, Jean-Luc 19 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 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 156 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 1,649 times in 1,069 Documents Cited by ▼ Year ▼ The incompressible limit of the non-isentropic Euler equations. Zbl 0974.76072Métivier, G.; Schochet, S. 129 2001 Stability of multidimensional shocks. Zbl 1017.35075Métivier, Guy 64 2001 Para-differential calculus and applications to the Cauchy problem for nonlinear systems. Zbl 1156.35002Métivier, Guy 63 2008 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066Métivier, Guy; Zumbrun, Kevin 49 2005 Coherent and focusing multidimensional nonlinear geometric optics. Zbl 0836.35087Joly, J.-L.; Métivier, G.; Rauch, J. 44 1995 Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Zbl 0815.35066Joly, J.-L.; Metivier, G.; Rauch, J. 42 1993 The block structure condition for symmetric hyperbolic systems. Zbl 1073.35525Métivier, Guy 42 2000 Fonction spectrale et valeurs propres d’une classe d’opérateurs non elliptiques. Zbl 0376.35012Metivier, Guy 41 1976 Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Zbl 1207.35082Alazard, Thomas; Métivier, Guy 38 2009 Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155Métivier, Guy; Zumbrun, Kevin 36 2005 Valeurs propres d’opérateurs définis par la restriction de systèmes variationnels à des sous-espaces. Zbl 0328.35029Métivier, Guy 36 1978 Analytic hypoellipticity for operators with multiple characteristics. Zbl 0455.35040Metivier, Guy 35 1981 Recent mathematical results and open problems about shallow water equations. Zbl 1291.35001Bresch, Didier; Desjardins, Benoît; Métivier, Guy 35 2007 Averaging theorems for conservative systems and the weakly compressible Euler equations. Zbl 1029.34035Métivier, G.; Schochet, S. 34 2003 Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 32 2006 Propagation de l’analyticité des solutions de systèmes hyperboliques non-linéaires. Zbl 0545.35063Alinhac, S.; Métivier, G. 32 1984 Une classe d’opérateurs non hypoelliptiques analytiques. Zbl 0455.35041Metivier, Guy 31 1980 Resonant one dimensional nonlinear geometric optics. Zbl 0851.35023Joly, J.-L.; Métivier, G.; Rauch, J. 30 1993 Hypoellipticite analytique sur des groupes nilpotents de rang 2. Zbl 0433.35015Metivier, Guy 30 1980 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 Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 29 2005 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 24 2010 Diffractive nonlinear geometric optics with rectification. Zbl 0928.35093Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 24 1998 Global solutions to Maxwell equations in a ferromagnetic medium. Zbl 0964.35155Joly, J. L.; Métivier, G.; Rauch, J. 23 2000 Valeurs propres de problèmes aux limites elliptiques irréguliers. Zbl 0401.35088Metivier, Guy 22 1977 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 21 2000 Remarks on the well-posedness of the nonlinear Cauchy problem. Zbl 1071.35074Métivier, Guy 21 2005 Transparent nonlinear geometric optics and Maxwell-Bloch equations. Zbl 1170.78311Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 20 2000 Focusing at a point and absorption of nonlinear oscillations. Zbl 0857.35087Joly, J. L.; Métivier, G.; Rauch, J. 20 1995 Propriété des iterés et ellipticite. Zbl 0388.35063Metivier, Guy 19 1978 Coherent nonlinear waves and the Wiener algebra. Zbl 0791.35019Joly, J.-L.; Métivier, G.; Rauch, J. 17 1994 The Cauchy problem for semilinear hyperbolic systems with discontinuous data. Zbl 0631.35056Metivier, Guy 16 1986 Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2005 Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations. Zbl 1099.35094Bresch, Didier; Métivier, Guy 16 2006 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 16 2008 Stability of multidimensional weak shocks. Zbl 0711.35078Métivier, Guy 15 1990 Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 14 2004 Small viscosity and boundary layer methods. Theory, stability analysis, and applications. Zbl 1133.35001Métivier, Guy 14 2004 Théorie spectrale des opérateurs uniformement elliptiques sur quelques ouverts irréguliers. Zbl 0251.35074Fleckinger, Jacqueline; Metivier, Guy 13 1973 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. 12 1986 Diffractive nonlinear geometric optics. Zbl 0910.35076Donnat, P.; Joly, J.-L.; Métivier, G.; Rauch, J. 12 1996 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 Analytic vectors of hypoelliptic operators of principal type. Zbl 0496.35026Baouendi, M. S.; Metivier, G. 11 1982 Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 11 2008 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. 10 1986 Non-hypoellipticite analytique pour D//\(x^ 2\) + (\(x^ 2\) + \(y^ 2)\) D//\(y^ 2\). Zbl 0481.35033Metivier, Guy 10 1981 Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332Métivier, G.; Zumbrun, K. 10 2004 A nonlinear instability for \(3\times 3\) systems of conservation laws. Zbl 0820.35093Joly, J. L.; Metivier, G.; Rauch, J. 10 1994 The mathematics of nonlinear optics. Zbl 1191.35263Métivier, Guy 10 2009 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 9 2018 Ondes soniques. (Sonic waves). Zbl 0728.35068Métivier, G. 9 1991 Instabilities in Zakharov equations for laser propagation in a plasma. Zbl 1133.35303Colin, Thierry; Métivier, Guy 9 2006 Progressing wave solutions to certain nonlinear mixed problems. Zbl 0613.35050Beals, Michael; Metivier, Guy 9 1986 A well-posedness result for hyperbolic operators with Zygmund coefficients. Zbl 1282.35220Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy 8 2013 Nonlinear oscillations beyond caustics. Zbl 0862.35066Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 8 1996 Global solvability of the anharmonic oscillator model from nonlinear optics. Zbl 0859.35124Joly, J. L.; Metivier, G.; Rauch, J. 8 1996 Reflection of transversal progressing waves in nonlinear strictly hyperbolic mixed problems. Zbl 0633.35051Beals, Michael; Métivier, Guy 8 1987 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 Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) Zbl 1091.35039Cheverry, Christophe; Guès, Olivier; Métivier, Guy 8 2003 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 8 2015 Nonlinear high frequency hyperbolic waves. Zbl 0824.35077Joly, J. L.; Metivier, G.; Rauch, J. 7 1992 Trilinear resonant interactions of semilinear hyperbolic waves. Zbl 0955.35007Métivier, G.; Schochet, S. 7 1998 Uniqueness and approximation of solutions of first order nonlinear equations. Zbl 0594.35018Metivier, Guy 7 1985 Kernels and symbols of analytic pseudodifferential operators. Zbl 0535.35081Baouendi, M. S.; Goulaouic, C.; Métivier, G. 7 1983 Anelastic limits for Euler-type systems. Zbl 1204.35117Bresch, Didier; Métivier, Guy 7 2010 Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems. Zbl 1133.35404Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 7 2007 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 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 \(L^2\) 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 Counterexamples to Hölmgren’s uniqueness for analytic nonlinear Cauchy problems. Zbl 0794.35026Métivier, G. 6 1993 Trilinear compensated compactness and nonlinear geometric optics. Zbl 0840.35013Joly, J. L.; Métivier, G.; Rauch, J. 6 1995 Caustics for dissipative semilinear oscillations. Zbl 0963.35114Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 6 2000 Rigorous resonant 1-d nonlinear geometric optics. Zbl 0718.35094Joly, J. L.; Métivier, G.; Rauch, J. 6 1990 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. 6 2009 Hypberbolic domains of determinacy and Hamilton-Jacobi equations. Zbl 1090.35114Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 6 2005 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 Large-amplitude high-frequency waves for quasilinear hyperbolic systems. Zbl 1107.35079Cheverry, C.; Guès, O.; Métivier, G. 5 2004 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 Problèmes mixtes non linéaires et stabilité des chocs multidimensionnels. (Nonlinear problems and stability of multidimensional shocks). Zbl 0659.35063Métivier, Guy 5 1987 Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems. Zbl 1316.35172Colombini, Ferruccio; Métivier, Guy 5 2015 Existence of semilinear relaxation shocks. Zbl 1180.35358Métivier, Guy; Zumbrun, Kevin 4 2009 Several recent results in nonlinear geometric optics. Zbl 0854.35115Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 4 1996 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 Comportement asymptotique des valeurs propres d’opérateurs elliptiques dégénérées. Zbl 0329.35047Metivier, Guy 4 1976 Dispersive stabilization. Zbl 1192.35165Métivier, Guy; Rauch, Jeffrey 4 2010 Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 4 2008 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 Incompressible limit of nonisentropic Euler equations. (Limite incompressible des équations d’Euler non isentropiques.) Zbl 1061.76074Métivier, Guy; Schochet, Steven 3 2001 Caustics for dissipative semilinear oscillations. Zbl 0891.35098Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 3 1997 Recent results in nonlinear geometric optics. Zbl 0938.35034Métivier, Guy; Joly, Jean-Luc; Rauch, Jeffrey 3 1999 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 Théorie spectrale d’opérateurs elliptiques sur des ouverts irréguliers. Zbl 0264.47040Metivier, G. 3 1973 Strictly dissipative nonuniqueness with corners. Zbl 1377.35193Métivier, Guy; Rauch, Jeffrey 2 2017 Problemes de Cauchy et ondes non linéaires. Zbl 0606.35051Metivier, Guy 2 1986 Une classe d’opérateurs non hypoelliptiques analytiques. Zbl 0419.35022Metivier, G. 2 1979 Waves interacting with a partially immersed obstacle in the Boussinesq regime. Zbl 07413798Bresch, Didier; Lannes, David; Métivier, Guy 2 2021 Waves interacting with a partially immersed obstacle in the Boussinesq regime. Zbl 07413798Bresch, Didier; Lannes, David; Métivier, Guy 2 2021 On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients. Zbl 1439.35317Colombini, 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 1406.35490Lannes, David; Métivier, Guy 9 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 8 2015 Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems. Zbl 1316.35172Colombini, 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 1332.35205Métivier, 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 24 2010 Anelastic limits for Euler-type systems. Zbl 1204.35117Bresch, Didier; Métivier, Guy 7 2010 Dispersive stabilization. Zbl 1192.35165Métivier, Guy; Rauch, Jeffrey 4 2010 Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Zbl 1207.35082Alazard, Thomas; Métivier, Guy 38 2009 The mathematics of nonlinear optics. Zbl 1191.35263Métivier, Guy 10 2009 Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Zbl 1197.76116Métivier, Guy; Zumbrun, K. 6 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 63 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 16 2008 Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 11 2008 Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 4 2008 Recent mathematical results and open problems about shallow water equations. Zbl 1291.35001Bresch, Didier; Desjardins, Benoît; Métivier, Guy 35 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 32 2006 Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations. Zbl 1099.35094Bresch, Didier; Métivier, Guy 16 2006 Instabilities in Zakharov equations for laser propagation in a plasma. Zbl 1133.35303Colin, Thierry; Métivier, Guy 9 2006 Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066Métivier, Guy; Zumbrun, Kevin 49 2005 Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155Métivier, Guy; Zumbrun, Kevin 36 2005 Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 29 2005 Remarks on the well-posedness of the nonlinear Cauchy problem. Zbl 1071.35074Métivier, Guy 21 2005 Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 16 2005 Hypberbolic domains of determinacy and Hamilton-Jacobi equations. Zbl 1090.35114Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 6 2005 Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin 14 2004 Small viscosity and boundary layer methods. Theory, stability analysis, and applications. Zbl 1133.35001Métivier, Guy 14 2004 Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332Métivier, G.; Zumbrun, K. 10 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. 5 2004 Averaging theorems for conservative systems and the weakly compressible Euler equations. Zbl 1029.34035Métivier, G.; Schochet, S. 34 2003 Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) Zbl 1091.35039Cheverry, Christophe; Guès, Olivier; Métivier, Guy 8 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. 129 2001 Stability of multidimensional shocks. Zbl 1017.35075Métivier, Guy 64 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 42 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 21 2000 Transparent nonlinear geometric optics and Maxwell-Bloch equations. Zbl 1170.78311Joly, Jean-Luc; Metivier, Guy; Rauch, Jeffrey 20 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 6 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 24 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. 2 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. 12 1996 Nonlinear oscillations beyond caustics. Zbl 0862.35066Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 8 1996 Global solvability of the anharmonic oscillator model from nonlinear optics. Zbl 0859.35124Joly, J. L.; Metivier, G.; Rauch, J. 8 1996 Several recent results in nonlinear geometric optics. Zbl 0854.35115Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey 4 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. 44 1995 Focusing at a point and absorption of nonlinear oscillations. Zbl 0857.35087Joly, J. L.; Métivier, G.; Rauch, J. 20 1995 Trilinear compensated compactness and nonlinear geometric optics. Zbl 0840.35013Joly, J. L.; Métivier, G.; Rauch, J. 6 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. 42 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 15 1990 Rigorous resonant 1-d nonlinear geometric optics. Zbl 0718.35094Joly, J. L.; Métivier, G.; Rauch, J. 6 1990 Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations. Zbl 0711.35080Métivier, Guy; Rauch, Jeffrey 5 1990 Théorème d’unicité pour des vecteurs analytiques. (Uniqueness theorem for analytic vectors). Zbl 0704.35031Bolley, Pierre; Camus, Jacques; Métivier, Guy 1 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. 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 0608.35026Bolley, P.; Camus, J.; Metivier, G. 10 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. 32 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. 7 1983 Estimation du reste en théorie spectrale. Zbl 0558.35050Metivier, Guy 1 1983 Estimation du reste en théorie spectrale. Zbl 0542.35055Métivier, Guy 1 1983 Analytic vectors of hypoelliptic operators of principal type. Zbl 0496.35026Baouendi, M. S.; Metivier, G. 11 1982 ...and 18 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 998 Authors 51 Zumbrun, Kevin R. 42 Métivier, Guy 28 Rauch, Jeffrey B. 19 Alazard, Thomas 17 Trakhinin, Yuri L. 17 Williams, Mark 16 Fan, Jishan 16 Guès, Olivier 15 Cheverry, Christophe 14 Chen, Hua 14 Himonas, A. Alexandrou 14 Li, Fucai 14 Wang, Ya-Guang 13 Carles, Rémi 13 Fanelli, Francesco 12 Chen, Gui-Qiang G. 12 Coulombel, Jean-François 11 Bove, Antonio 11 Chen, Shuxing 11 Derridj, Makhlouf 11 Tartakoff, David S. 11 Zhu, Shengguo 10 Del Santo, Daniele 10 Lannes, David 10 Petronilho, Gerson 9 Bresch, Didier 9 Colin, Thierry 9 Ju, Qiangchang 9 Li, Dening 9 Morando, Alessandro 9 Rousset, Frédéric 9 Schochet, Steven H. 9 Texier, Benjamin 9 Trebeschi, Paola 8 Nakamura, Gen 8 Ou, Yaobin 8 Secchi, Paolo 8 Temam, Roger Meyer 8 Xin, Zhouping 8 Zhang, Zhifei 7 Colombini, Ferruccio 7 Freistühler, Heinrich 7 Joly, Jean-Luc 7 Masmoudi, Nader 7 Nguyen, Toan Trong 7 Wang, Tao 7 Wang, Yaguang 7 Yin, Huicheng 6 Barker, Blake 6 Benoit, Antoine 6 Chen, Hongge 6 Chinni, Gregorio 6 Cordaro, Paulo D. 6 Godin, Paul 6 Hanges, Nicholas William 6 Humpherys, Jeffrey 6 Jiang, Song 6 Lapidus, Michel L. 6 Montalto, Riccardo 6 Mughetti, Marco 6 Nguyen, Huy Quang 6 Rothschild, Linda Preiss 6 Sueur, Franck 6 Tang, Tong 6 Wang, Dehua 6 Xiang, Wei 6 Xie, Chunjing 6 Zhou, Yong 5 Barsukow, Wasilij 5 Benzoni-Gavage, Sylvie 5 Berti, Massimiliano 5 Burq, Nicolas 5 Christ, Michael 5 Desjardins, Benoît 5 Duchêne, Vincent 5 Gallagher, Isabelle 5 Helffer, Bernard 5 Junca, Stéphane 5 Li, Jingna 5 Lyng, Gregory Daniel 5 Strani, Marta 5 Trélat, Emmanuel 5 Zhang, Ping 5 Zuily, Claude 4 Albano, Paolo 4 Alinhac, Serge 4 Audiard, Corentin 4 Babin, Anatoli V. 4 Baldi, Pietro 4 Chen, Robin Ming 4 Cheng, Bin 4 Cicognani, Massimo 4 Cimrák, Ivan 4 Dumas, Éric 4 Fang, Beixiang 4 Feireisl, Eduard 4 Feola, Roberto 4 Fleckinger, Jacqueline 4 Gallice, Gérard 4 Grenier, Emmanuel ...and 898 more Authors all top 5 Cited in 214 Serials 89 Journal of Differential Equations 70 Archive for Rational Mechanics and Analysis 66 Communications in Partial Differential Equations 24 Journal de Mathématiques Pures et Appliquées. 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(English Edition) 4 Analysis & PDE 4 Complex Analysis and its Synergies 4 Water Waves 3 Computers and Fluids 3 Computers & Mathematics with Applications 3 Journal d’Analyse Mathématique 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 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 Annales Henri Poincaré 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Journal of the Institute of Mathematics of Jussieu 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. 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English Series 2 Revista Matemática Iberoamericana ...and 114 more Serials all top 5 Cited in 44 Fields 965 Partial differential equations (35-XX) 451 Fluid mechanics (76-XX) 69 Optics, electromagnetic theory (78-XX) 46 Global analysis, analysis on manifolds (58-XX) 46 Numerical analysis (65-XX) 38 Operator theory (47-XX) 37 Statistical mechanics, structure of matter (82-XX) 31 Mechanics of deformable solids (74-XX) 26 Dynamical systems and ergodic theory (37-XX) 24 Differential geometry (53-XX) 22 Topological groups, Lie groups (22-XX) 21 Ordinary differential equations (34-XX) 21 Quantum theory (81-XX) 20 Several complex variables and analytic spaces (32-XX) 20 Functional analysis (46-XX) 19 Classical thermodynamics, heat transfer (80-XX) 19 Geophysics (86-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 14 Real functions (26-XX) 12 Abstract harmonic analysis (43-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 12 Probability theory and stochastic processes (60-XX) 10 Systems theory; control (93-XX) 7 Relativity and gravitational theory (83-XX) 6 Measure and integration (28-XX) 6 Functions of a complex variable (30-XX) 6 Astronomy and astrophysics (85-XX) 5 Nonassociative rings and algebras (17-XX) 4 Mechanics of particles and systems (70-XX) 4 Biology and other natural sciences (92-XX) 3 Number theory (11-XX) 3 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 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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