@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},
year = {2000},
publisher = {Soci\'et\'e math\'ematique de France},
number = {268},
mrnumber = {1787068},
zbl = {0996.35001},
language = {fr},
url = {https://www.numdam.org/item/AST_2000__268__R1_0/}
}
TY - BOOK AU - Francheteau, Jacques AU - Métivier, Guy TI - Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels T3 - Astérisque PY - 2000 IS - 268 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2000__268__R1_0/ LA - fr ID - AST_2000__268__R1_0 ER -
Francheteau, Jacques; Métivier, Guy. Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels. Astérisque, no. 268 (2000), 206 p. https://www.numdam.org/item/AST_2000__268__R1_0/
[Al] , Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations, 14 (1989), pp 173-230. | MR | Zbl | DOI
[Al-Gé] , , Opérateurs pseudodifférentiels et théorème de Nash-Moser, InterEditions Editions du CNRS., Paris, 1991. | MR | Zbl
[Ar-Ma] , , Nonlinear development of instabilities in supersonic vortex sheets I. The basic kink mode, Physica D, 28 (1987), pp 253-281. | MR | Zbl | DOI
[Bo] , 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. | MR | Zbl | EuDML | Numdam | DOI
[BCP] , , , Well-posedness of the Cauchy problem for systems of conservation laws, Mem. Amer. Math. Soc, à paraître. | MR | Zbl
[Ch-Pi] , , Introduction à la théorie des équations aux dérivées partielles linéaires, Bordas, Paris, 1981. | MR | Zbl
[Co-Fr] , , Supersonic flow and shock waves, Wiley-Interscience, New York, 1948. | MR | Zbl
[Co-Hi] , , Methods of Mathematical Physics, John Wiley & Sons, New York, 1962. | Zbl | MR
[Fr1] , Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math., 7 (1954), pp 345-392. | MR | Zbl | DOI
[Fr2] , Symmetric positive linear differential equations, Comm. Pure Appl. Math., 11 (1958), pp 333-418. | MR | Zbl | DOI
[Fr-La1] , Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sc. USA, 68 (1971), pp 1686-1688. | MR | Zbl | DOI
[Fr-La2] , Boundary value problems for first order operators, Comm. Pure Appl. Math., 18 (1965), pp 355-388. | MR | Zbl | DOI
[Gå] , 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. | MR | Zbl
[Gl] , Solutions in the large, for nonlinear systems of conservation laws, Comm. Pure Appl. Math., 18 (1965), pp 685-715. | Zbl | MR | DOI
[Go-Ra] , , Hyperbolic systems of conservation laws vol 3-4, Mathématiques & Applications, Ellipses, Paris, 1991. | MR | Zbl
[Gu] , Problèmes mixtes hyperboliques quasilinéaires, Comm. Partial Differential Equations, 15 (1990) pp 595-645. | MR | Zbl
[Ha] , A convergent séries expansion for hyperbolic systems of conservation laws, Trans. Amer. Math. Soc, 294 (1986), pp 383-424. | MR | Zbl | DOI
[He] , Régularité des solutions du problème de Riemann, Comm. Partial Differential Equations, 15 (1990), pp 693-709. | MR | Zbl | DOI
[Hö1] , The boundary problem of physical geodesy, Arch. Rational Mech. Anal., 62 (1976), pp 1-52. | MR | Zbl | DOI
[Hö2] , Lectures on nonlinear hyperbolic differential equations, Springer Verlag, 1996. | Zbl | MR
[Kr] , Initial boundary value Problem for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), pp 277-298. | MR | Zbl | DOI
[La] , Hyperbolic systems of conservation laws, Comm. Pure Appl. Math., 10 (1957), pp 537-566. | MR | Zbl | DOI
[La-Ph] , , Local Boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math., 13 (1960), pp 427-455. | MR | Zbl | DOI
[Li] , Boundary value problems for quasilinear hyperbolic systems, Math. Series V., Duke Univ., Durham, 1985. | MR | Zbl
[Li-Ma] , , Problèmes aux limites non homogènes, Dunod, Paris, 1968. | MR | Zbl
[Ma1] , The stability of multidimensional shock fronts, Mem. Amer. Math. Soc., n° 275, 1983. | MR | Zbl
[Ma2] , The existence of multidimensional shock fronts, Mem. Amer. Math. Soc., n° 281, 1983. | MR | Zbl
[Ma3] , Compressible fluid flows and systems of conservation laws, Applied Math. Sc., 53, Springer Verlag, 1984. | Zbl | MR | DOI
[Ma-Os] , , Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math., 28 (1975), pp 607-676. | MR | Zbl | DOI
[Ma-Ra] , , Differentiability of solutions to hyperbolic initial boundary value problems, Trans. Amer. Math. Soc., 189 (1974), pp 303-318. | MR | Zbl
[Mey] , Remarques sur un théorème de J.-M. Bony, Suppl. ai Rend, del Circolo Mat. di Palermo, II, 1 (1981) pp 1.20. | MR | Zbl
[Mé1] , Ondes soniques, J. Math, pures et appl., 70 (1991), pp 197-268. | MR | Zbl
[Mé2] , Stability of multidimensional weak shocks, Comm. Partial Differential Equations, 15 (1990), pp 983-1028. | MR | Zbl | DOI
[Mé3] , 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. | MR | Zbl | DOI
[Mé4] , Stability of multidimensional shocks, Lecture notes, Kochel summer school, 1999, à paraître dans Recent Advances in the Theory of Shock Waves, PNLDE, Birkauser. | Zbl | MR
[Mé5] , The Cauchy problem for semi-linear hyperbolic systems with discontinuous data, Duke Math. J., 53 (1986), pp 983-1011. | MR | Zbl
[Mé-Ra] , , Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations, Comm. Partial Differential Equations, 15 (1990), pp 1079-1140. | MR | Zbl | DOI
[Mok] , Problèmes mixtes hyperboliques non linéaires, Thèse Université de Rennes, 1987.
[Mos] , A rapidly convergent iteration method and nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa, 20 (1966), pp 499-535. | MR | Zbl | EuDML | Numdam
[Na] , The embedding problem for Riemannian manifolds, Ann. of Math., 63 (1956), pp 20-63. | MR | Zbl | DOI
[Pe] , On the differentiablity of solutions of symmetric hyperbolic systems, Proc. Amer. Math. Soc., 14 (1963), pp 963-969. | MR | Zbl | DOI
[Ra] , Symmetric positive systems with boundary characteristic of constant multiplicity, Trans. Amer. Math. Soc., 291 (1985), pp 167-187. | MR | Zbl | DOI
[Ral] , Note on a paper of Kreiss, Comm. Pure Appl. Math., 24 (1971), pp 759-762. | MR | DOI
[Ra-Re] , , Discontinuous progressing waves for semi-linear systems, Comm. Partial Differential Equations, 10, (1985), pp 1033-1075. | MR | Zbl | DOI
[Sab] , Ondes de gradients multidimensionnelles, Mem. Amer. Math. Soc., n° 511, 1993. | MR | Zbl
[Sar] , Differentiable solutions of symmetrizable and singular symmetric first order systems, Arch. Rational Mech. Anal., 26 (1967), pp 357-384. | MR | Zbl | DOI
[Se] , Systèmes de lois de conservation I et II, Diderot Editeur, Paris, New York, Amsterdam, 1996. | MR
[Ta] , Regularity of solutions to boundary value problems for first order systems, Indiana Univ. Math. J., 21 (1972), pp 1113-1129. | MR | Zbl | DOI
[Ts] , Analyticity of solutions of hyperbolic mixed problems, J. Math. Kyoto Univ, 13 (1973), pp 323-371. | MR | Zbl






