@article{AIHPC_2004__21_4_401_0,
author = {Coulombel, Jean-Fran\c cois},
title = {Weakly stable multidimensional shocks},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {21},
year = {2004},
pages = {401-443},
doi = {10.1016/j.anihpc.2003.04.001},
mrnumber = {2069632},
zbl = {1072.35120},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_4_401_0}
}
Coulombel, Jean-François. Weakly stable multidimensional shocks. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 401-443. doi : 10.1016/j.anihpc.2003.04.001. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_4_401_0/
[1] , Sobolev Spaces, Academic Press, 1975. | MR 450957 | Zbl 0314.46030
[2] , Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations 14 (2) (1989) 173-230. | MR 976971 | Zbl 0692.35063
[3] , Blowup for Nonlinear Hyperbolic Equations, Birkhäuser, Boston, 1995. | MR 1339762 | Zbl 0820.35001
[4] , Ordinary Differential Equations, Springer-Verlag, 1992. | MR 1162307 | Zbl 0744.34001
[5] , Stability of multi-dimensional phase transitions in a van der Waals fluid, Nonlinear Anal. 31 (1-2) (1998) 243-263. | MR 1487544 | Zbl 0928.76015
[6] , Stability of subsonic planar phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal. 150 (1) (1999) 23-55. | MR 1738168 | Zbl 0980.76023
[7] , , , , Generic types and transitions in hyperbolic initial-boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A 132 (2002) 1073-1104. | MR 1938714 | Zbl 1029.35165
[8] S. Benzoni-Gavage, D. Serre, First order systems of hyperbolic partial differential equations with applications, in preparation.
[9] , , Stability of fast parallel MHD shock waves in polytropic gas, Eur. J. Mech. B Fluids 18 (2) (1999) 197-211. | MR 1681896 | Zbl 0940.76019
[10] , 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. | Numdam | MR 631751 | Zbl 0495.35024
[11] , , Introduction to the Theory of Linear Partial Differential Equations, North-Holland, 1982. | MR 678605 | Zbl 0487.35002
[12] , Weak stability of nonuniformly stable multidimensional shocks, SIAM J. Math. Anal. 34 (1) (2002) 142-172. | MR 1950830 | Zbl 1029.35171
[13] , Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, 2000. | MR 1763936 | Zbl 0940.35002
[14] , , Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Astérisque, vol. 268, 2000. | MR 1787068 | Zbl 0996.35001
[15] , Some results on the stability of non-classical shock waves, J. Partial Differential Equations 111 (1) (1998) 25-38. | MR 1618406 | Zbl 0903.35006
[16] , , , 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 1850311 | Zbl 1002.35087
[17] , Mixed problems in several variables, J. Math. Mech. 12 (1963) 317-334. | MR 147790 | Zbl 0149.06602
[18] , Differential Topology, Springer-Verlag, 1994. | MR 1336822 | Zbl 0356.57001
[19] , Lectures on Nonlinear Hyperbolic Differential Equations, Springer-Verlag, 1997. | MR 1466700 | Zbl 0881.35001
[20] , Perturbation Theory for Linear Operators, Springer-Verlag, 1976. | MR 407617 | Zbl 0342.47009 | Zbl 0148.12601
[21] , Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970) 277-298. | MR 437941 | Zbl 0188.41102 | Zbl 0193.06902
[22] , Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957) 537-566. | MR 93653 | Zbl 0081.08803
[23] , The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 43 (281) (1983). | MR 699241 | Zbl 0517.76068
[24] , The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 41 (275) (1983). | MR 683422 | Zbl 0506.76075
[25] , Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Springer-Verlag, 1984. | MR 748308 | Zbl 0537.76001
[26] , The block structure condition for symmetric hyperbolic systems, Bull. London Math. Soc. 32 (6) (2000) 689-702. | MR 1781581 | Zbl 1073.35525
[27] , Stability of multidimensional shocks, in: Advances in the Theory of Shock Waves, Birkhäuser, 2001, pp. 25-103. | MR 1842775 | Zbl 1017.35075
[28] , Remarques sur un théorème de J.M. Bony, Suppl. Rend. Circ. Mat. Palermo Ser. II 1 (1981) 1-20. | MR 639462 | Zbl 0473.35021
[29] A. Mokrane, Problèmes mixtes hyperboliques non-linéaires, Ph.D. Thesis, Université de Rennes I, 1987.
[30] , , On structures of certain L2-well-posed mixed problems for hyperbolic systems of first order, Hokkaido Math. J. 4 (1975) 82-158. | MR 380131 | Zbl 0304.35067
[31] , Note on a paper of Kreiss, Comm. Pure Appl. Math. 24 (6) (1971) 759-762. | MR 606239 | Zbl 0215.16802
[32] , Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension 2, Arch. Rational Mech. Anal. 101 (3) (1988) 261-292. | MR 930125 | Zbl 0652.73019
[33] , Systems of Conservation Laws. 1, Cambridge University Press, 1999. | MR 1707279 | Zbl 0930.35001
[34] , Systems of Conservation Laws. 2, Cambridge University Press, 2000. | MR 1775057 | Zbl 0936.35001
[35] , La transition vers l'instabilité pour les ondes de choc multi-dimensionnelles, Trans. Amer. Math. Soc. 353 (12) (2001) 5071-5093. | MR 1852095 | Zbl 1078.35521