Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels

Resume Pour des systemes generaux de lois de conservation, en dimension quelconque d'espace, nous prouvons l'existence de chocs faibles relatifs a une valeur propre simple vraiment non lineaire du systeme et pour un temps d'existence T independant de la force du choc. En particulier, les resultats s'appliquent au systeme d'Euler de la dynamique des gaz.

[1]  L. Sarason.  Differentiable solutions of symmetrizable and singular symmetric first order systems , 1967 .

[2]  Kurt Friedrichs,et al.  Boundary value problems for first order operators , 1965 .

[3]  R. Phillips,et al.  Local boundary conditions for dissipative symmetric linear differential operators , 1960 .

[4]  P. Gérard,et al.  Opérateurs pseudo-différentiels et théorème de Nash-Moser , 1991 .

[5]  F. Massey,et al.  Differentiability of solutions to hyperbolic initial-boundary value problems , 1974 .

[6]  A. Mokrane.  Problemes mixtes hyperboliques non lineaires , 1987 .

[7]  Jürgen Moser,et al.  A rapidly convergent iteration method and non-linear differential equations = II , 1966 .

[8]  M. Reed,et al.  Discontinuous progressing waves for semilinear systems , 1985 .

[9]  B. M. Fulk.  MATH , 1992 .

[10]  L. Hörmander,et al.  Lectures on Nonlinear Hyperbolic Differential Equations , 1997 .

[11]  Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations , 1990 .

[12]  Kurt Friedrichs,et al.  Symmetric positive linear differential equations , 1958 .

[13]  Gideon Peyser.  On the differentiability of solutions of symmetric hyperbolic systems , 1963 .

[14]  Jeffrey Rauch,et al.  Symmetric positive systems with boundary characteristic of constant multiplicity , 1985 .

[15]  J. Bony,et al.  Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires , 1980 .

[16]  A. Majda,et al.  The stability of multidimensional shock fronts , 1983 .

[17]  J. Ralston.  Note on a paper of Kreiss , 1971 .

[18]  Eduard Harabetian,et al.  A convergent series expansion for hyperbolic systems of conservation laws , 1986 .

[19]  Andrew J. Majda,et al.  Initial‐boundary value problems for hyperbolic equations with uniformly characteristic boundary , 1975 .

[20]  J. Nash.  The imbedding problem for Riemannian manifolds , 1956 .

[21]  A. Heibig.  Regularite Des Solutions Du Probleme De Riemann , 1990 .

[22]  S. Alinhac,et al.  Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels , 1989 .

[23]  A. Majda,et al.  The existence of multidimensional shock fronts , 1983 .

[24]  M. Balazard,et al.  REMARQUES SUR UN TH ´ EOR ` EME DE , 1989 .

[25]  G. Métivier.  The Cauchy problem for semilinear hyperbolic systems with discontinuous data , 1986 .

[26]  P. Lax.  Hyperbolic systems of conservation laws II , 1957 .

[27]  M. Tsuji.  Analyticity of solutions of hyperbolic mixed problems , 1973 .

[28]  J. A. Salvato.  John wiley & sons. , 1994, Environmental science & technology.

[29]  Andrew J. Majda,et al.  Nonlinear development of instabilities in supersonic vortex sheets I. The basic kink modes , 1987 .

[30]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[31]  Tatsien Li,et al.  Boundary value problems for quasilinear hyperbolic systems , 1985 .

[32]  G. Métivier.  Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d'espace , 1986 .