Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels
Astérisque, no. 268 (2000) , 206 p.
@book{AST_2000__268__R1_0,
     author = {Francheteau, Jacques and M\'etivier, Guy},
     title = {Existence de chocs faibles pour des syst\`emes quasi-lin\'eaires hyperboliques multidimensionnels},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {268},
     year = {2000},
     zbl = {0996.35001},
     mrnumber = {1787068},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2000__268__R1_0/}
}
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Francheteau, Jacques; Métivier, Guy. Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels. Astérisque, no. 268 (2000), 206 p. http://numdam.org/item/AST_2000__268__R1_0/

[Al] S. Alinhac, Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations, 14 (1989), pp 173-230. | DOI | Zbl | MR

[Al-Gé] S. Alinhac, P. Gérard, Opérateurs pseudodifférentiels et théorème de Nash-Moser, InterEditions Editions du CNRS., Paris, 1991. | Zbl | MR

[Ar-Ma] M. Artola, A. Majda, Nonlinear development of instabilities in supersonic vortex sheets I. The basic kink mode, Physica D, 28 (1987), pp 253-281. | DOI | Zbl | MR

[Bo] J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. scient. Éc. Norm. Sup. 4e série, 14 (1981) pp 209-246. | DOI | Numdam | EuDML | Zbl | MR

[BCP] A. Bressan, G. Crasta, B. Piccoli, Well-posedness of the Cauchy problem for n×n systems of conservation laws, Mem. Amer. Math. Soc, à paraître. | Zbl | MR

[Ch-Pi] J. Chazarain, A. Piriou, Introduction à la théorie des équations aux dérivées partielles linéaires, Bordas, Paris, 1981. | Zbl | MR

[Co-Fr] R. Courant, K. O. Friedrichs, Supersonic flow and shock waves, Wiley-Interscience, New York, 1948. | Zbl | MR

[Co-Hi] R. Courant, D. Hilbert, Methods of Mathematical Physics, John Wiley & Sons, New York, 1962. | MR | Zbl

[Fr1] K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math., 7 (1954), pp 345-392. | DOI | Zbl | MR

[Fr2] K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math., 11 (1958), pp 333-418. | DOI | Zbl | MR

[Fr-La1] K. O. Friedrichs, P. Lax Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sc. USA, 68 (1971), pp 1686-1688. | DOI | Zbl | MR

[Fr-La2] K. O. Friedrichs, P. Lax Boundary value problems for first order operators, Comm. Pure Appl. Math., 18 (1965), pp 355-388. | DOI | Zbl | MR

[Gå] L. Gårding, Problèmes de Cauchy pour des systèmes quasi-linéaires d'ordre un, strictement hyperboliques, dans Les EDP, Colloques Internationaux du CNRS, vol 117, (1963), pp 33-40. | Zbl | MR

[Gl] J. Glimm, Solutions in the large, for nonlinear systems of conservation laws, Comm. Pure Appl. Math., 18 (1965), pp 685-715. | DOI | MR | Zbl

[Go-Ra] E. Godlewski, P. A. Raviart, Hyperbolic systems of conservation laws vol 3-4, Mathématiques & Applications, Ellipses, Paris, 1991. | Zbl | MR

[Gu] O. Guès, Problèmes mixtes hyperboliques quasilinéaires, Comm. Partial Differential Equations, 15 (1990) pp 595-645. | Zbl | MR

[Ha] E. Harabetian, A convergent séries expansion for hyperbolic systems of conservation laws, Trans. Amer. Math. Soc, 294 (1986), pp 383-424. | DOI | Zbl | MR

[He] A. Heibig, Régularité des solutions du problème de Riemann, Comm. Partial Differential Equations, 15 (1990), pp 693-709. | DOI | Zbl | MR

[Hö1] L. Hörmander, The boundary problem of physical geodesy, Arch. Rational Mech. Anal., 62 (1976), pp 1-52. | DOI | Zbl | MR

[Hö2] L. Hörmander, Lectures on nonlinear hyperbolic differential equations, Springer Verlag, 1996. | MR | Zbl

[Kr] H. O. Kreiss, Initial boundary value Problem for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), pp 277-298. | DOI | Zbl | MR

[La] P. Lax, Hyperbolic systems of conservation laws, Comm. Pure Appl. Math., 10 (1957), pp 537-566. | DOI | Zbl | MR

[La-Ph] P. Lax, R. S. Phillips, Local Boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math., 13 (1960), pp 427-455. | DOI | Zbl | MR

[Li] Li Ta Tsien, Boundary value problems for quasilinear hyperbolic systems, Math. Series V., Duke Univ., Durham, 1985. | Zbl | MR

[Li-Ma] J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes, Dunod, Paris, 1968. | Zbl | MR

[Ma1] A. Majda, The stability of multidimensional shock fronts, Mem. Amer. Math. Soc., n° 275, 1983. | Zbl | MR

[Ma2] A. Majda, The existence of multidimensional shock fronts, Mem. Amer. Math. Soc., n° 281, 1983. | Zbl | MR

[Ma3] A. Majda, Compressible fluid flows and systems of conservation laws, Applied Math. Sc., 53, Springer Verlag, 1984. | DOI | MR | Zbl

[Ma-Os] A. Majda, S. Osher, Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math., 28 (1975), pp 607-676. | DOI | Zbl | MR

[Ma-Ra] F. Massey, J. Rauch, Differentiability of solutions to hyperbolic initial boundary value problems, Trans. Amer. Math. Soc., 189 (1974), pp 303-318. | Zbl | MR

[Mey] Y. Meyer, Remarques sur un théorème de J.-M. Bony, Suppl. ai Rend, del Circolo Mat. di Palermo, II, 1 (1981) pp 1.20. | Zbl | MR

[Mé1] G. Métivier, Ondes soniques, J. Math, pures et appl., 70 (1991), pp 197-268. | Zbl | MR

[Mé2] G. Métivier, Stability of multidimensional weak shocks, Comm. Partial Differential Equations, 15 (1990), pp 983-1028. | DOI | Zbl | MR

[Mé3] G. Métivier, Interaction de deux chocs pour un système de deux lois de conservation en dimension deux d'espace, Trans. Amer. Math. Soc., 296 (1986), pp 431-479. | DOI | Zbl | MR

[Mé4] G. Métivier, Stability of multidimensional shocks, Lecture notes, Kochel summer school, 1999, à paraître dans Recent Advances in the Theory of Shock Waves, PNLDE, Birkauser. | MR | Zbl

[Mé5] G. Métivier, The Cauchy problem for semi-linear hyperbolic systems with discontinuous data, Duke Math. J., 53 (1986), pp 983-1011. | Zbl | MR

[Mé-Ra] G. Métivier, J. Rauch, Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations, Comm. Partial Differential Equations, 15 (1990), pp 1079-1140. | DOI | Zbl | MR

[Mok] A. Mokrane, Problèmes mixtes hyperboliques non linéaires, Thèse Université de Rennes, 1987.

[Mos] J. Moser, A rapidly convergent iteration method and nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa, 20 (1966), pp 499-535. | Numdam | EuDML | Zbl | MR

[Na] J. Nash, The embedding problem for Riemannian manifolds, Ann. of Math., 63 (1956), pp 20-63. | DOI | Zbl | MR

[Pe] G. Peyser, On the differentiablity of solutions of symmetric hyperbolic systems, Proc. Amer. Math. Soc., 14 (1963), pp 963-969. | DOI | Zbl | MR

[Ra] J. Rauch, Symmetric positive systems with boundary characteristic of constant multiplicity, Trans. Amer. Math. Soc., 291 (1985), pp 167-187. | DOI | Zbl | MR

[Ral] J. Ralston, Note on a paper of Kreiss, Comm. Pure Appl. Math., 24 (1971), pp 759-762. | DOI | MR

[Ra-Re] J. Rauch, M. Reed, Discontinuous progressing waves for semi-linear systems, Comm. Partial Differential Equations, 10, (1985), pp 1033-1075. | DOI | Zbl | MR

[Sab] M. Sablé-Tougeron, Ondes de gradients multidimensionnelles, Mem. Amer. Math. Soc., n° 511, 1993. | Zbl | MR

[Sar] L. Sarason, Differentiable solutions of symmetrizable and singular symmetric first order systems, Arch. Rational Mech. Anal., 26 (1967), pp 357-384. | DOI | Zbl | MR

[Se] D. Serre, Systèmes de lois de conservation I et II, Diderot Editeur, Paris, New York, Amsterdam, 1996. | MR

[Ta] D. Tartakoff, Regularity of solutions to boundary value problems for first order systems, Indiana Univ. Math. J., 21 (1972), pp 1113-1129. | DOI | Zbl | MR

[Ts] M. Tsuji, Analyticity of solutions of hyperbolic mixed problems, J. Math. Kyoto Univ, 13 (1973), pp 323-371. | Zbl | MR