Weakly stable multidimensional shocks

Coulombel, Jean-François

doi:10.1016/j.anihpc.2003.04.001

Coulombel, Jean-François

Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 4, pp. 401-443.

EuDML MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.anihpc.2003.04.001

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     author = {Coulombel, Jean-Fran\c{c}ois},
     title = {Weakly stable multidimensional shocks},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {401--443},
     publisher = {Elsevier},
     volume = {21},
     number = {4},
     year = {2004},
     doi = {10.1016/j.anihpc.2003.04.001},
     mrnumber = {2069632},
     zbl = {1072.35120},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.04.001/}
}

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Coulombel, Jean-François. Weakly stable multidimensional shocks. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 4, pp. 401-443. doi : 10.1016/j.anihpc.2003.04.001. http://www.numdam.org/articles/10.1016/j.anihpc.2003.04.001/

Bibliographie
Cité par

[1] Adams R.A, Sobolev Spaces, Academic Press, 1975. | MR | Zbl

[2] Alinhac S, Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations 14 (2) (1989) 173-230. | MR | Zbl

[3] Alinhac S, Blowup for Nonlinear Hyperbolic Equations, Birkhäuser, Boston, 1995. | MR | Zbl

[4] Arnol'D V.I, Ordinary Differential Equations, Springer-Verlag, 1992. | MR | Zbl

[5] Benzoni-Gavage S, Stability of multi-dimensional phase transitions in a van der Waals fluid, Nonlinear Anal. 31 (1-2) (1998) 243-263. | MR | Zbl

[6] Benzoni-Gavage S, Stability of subsonic planar phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal. 150 (1) (1999) 23-55. | MR | Zbl

[7] Benzoni-Gavage S, Rousset F, Serre D, Zumbrun K, Generic types and transitions in hyperbolic initial-boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A 132 (2002) 1073-1104. | MR | Zbl

[8] S. Benzoni-Gavage, D. Serre, First order systems of hyperbolic partial differential equations with applications, in preparation.

[9] Blokhin A.M, Trakhinin Y.L, Stability of fast parallel MHD shock waves in polytropic gas, Eur. J. Mech. B Fluids 18 (2) (1999) 197-211. | MR | Zbl

[10] Bony J.M, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4) 14 (2) (1981) 209-246. | EuDML | Numdam | MR | Zbl

[11] Chazarain J, Piriou A, Introduction to the Theory of Linear Partial Differential Equations, North-Holland, 1982. | MR | Zbl

[12] Coulombel J.F, Weak stability of nonuniformly stable multidimensional shocks, SIAM J. Math. Anal. 34 (1) (2002) 142-172. | MR | Zbl

[13] Dafermos C.M, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, 2000. | MR | Zbl

[14] Francheteau J, Métivier G, Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Astérisque, vol. 268, 2000. | Numdam | MR | Zbl

[15] Freistühler H, Some results on the stability of non-classical shock waves, J. Partial Differential Equations 111 (1) (1998) 25-38. | MR | Zbl

[16] Freistühler H, Fries C, Rohde C, Existence, bifurcation, and stability of profiles for classical and non-classical shock waves, in: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer, 2001, pp. 287-309, 814. | MR | Zbl

[17] Hersh R, Mixed problems in several variables, J. Math. Mech. 12 (1963) 317-334. | MR | Zbl

[18] Hirsch M.W, Differential Topology, Springer-Verlag, 1994. | MR | Zbl

[19] Hörmander L, Lectures on Nonlinear Hyperbolic Differential Equations, Springer-Verlag, 1997. | MR | Zbl

[20] Kato T, Perturbation Theory for Linear Operators, Springer-Verlag, 1976. | MR | Zbl

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

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

[23] Majda A, The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 43 (281) (1983). | MR | Zbl

[24] Majda A, The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 41 (275) (1983). | MR | Zbl

[25] Majda A, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Springer-Verlag, 1984. | MR | Zbl

[26] Métivier G, The block structure condition for symmetric hyperbolic systems, Bull. London Math. Soc. 32 (6) (2000) 689-702. | MR | Zbl

[27] Métivier G, Stability of multidimensional shocks, in: Advances in the Theory of Shock Waves, Birkhäuser, 2001, pp. 25-103. | MR | Zbl

[28] Meyer Y, Remarques sur un théorème de J.M. Bony, Suppl. Rend. Circ. Mat. Palermo Ser. II 1 (1981) 1-20. | MR | Zbl

[29] A. Mokrane, Problèmes mixtes hyperboliques non-linéaires, Ph.D. Thesis, Université de Rennes I, 1987.

[30] Ohkubo T, Shirota T, On structures of certain L²-well-posed mixed problems for hyperbolic systems of first order, Hokkaido Math. J. 4 (1975) 82-158. | MR | Zbl

[31] Ralston J.V, Note on a paper of Kreiss, Comm. Pure Appl. Math. 24 (6) (1971) 759-762. | MR | Zbl

[32] Sablé-Tougeron M, Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension 2, Arch. Rational Mech. Anal. 101 (3) (1988) 261-292. | MR | Zbl

[33] Serre D, Systems of Conservation Laws. 1, Cambridge University Press, 1999. | MR | Zbl

[34] Serre D, Systems of Conservation Laws. 2, Cambridge University Press, 2000. | MR | Zbl

[35] Serre D, La transition vers l'instabilité pour les ondes de choc multi-dimensionnelles, Trans. Amer. Math. Soc. 353 (12) (2001) 5071-5093. | MR | Zbl

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