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Transactions of the American Mathematical Society

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Double shock fronts for hyperbolic systems of conservation laws in multidimensional space

Authors: An Ton Bui and De Ning Li
Journal: Trans. Amer. Math. Soc. 316 (1989), 233-250
MSC: Primary 35L65; Secondary 76L05
MathSciNet review: 935939
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Abstract: The existence of a unique double shock front for hyperbolic systems of conservation laws in several space variables is established, extending an earlier result of Metivier. An example of a double shock wave arising from physical applications is given.

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  • [1] M. Beals and M. C. Reed, Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems, Trans. Amer. Math. Soc. 285 (1984), 159-184. MR 748836 (86a:35156)
  • [2] E. Harabetian, A convergent expansion for hyperbolic systems of conservation laws, Trans. Amer. Math. Soc. 294 (1986), 383-424. MR 825712 (87k:35160)
  • [3] T. Kato, The Cauchy problem for quasilinear symmetric hyperbolic systems, Arch. Rational Mech. Anal. 58 (1975), 181-205. MR 0390516 (52:11341)
  • [4] Dening Li, The nonlinear initial-boundary value problem and the existence of multidimensional shock wave for quasilinear hyperbolic-parabolic coupled systems, Chinese Ann. Math. 8B (1987), 252-280. MR 901389 (89d:35114)
  • [5] -, The $ {L^2}$-boundedness of pseudo-differential operators with nonsmooth coefficient symbols, (preprint). MR 0477884 (57:17385)
  • [6] A. Majda, The stability of multidimensional shock fronts--a new problem for linear hyperbolic equations, Mem. Amer. Math. Soc. 273 (1983). MR 683422 (84e:35100)
  • [7] -, The existence of multidimensional shock fronts, Mem. Amer. Math. Soc. 281 (1983). MR 699241 (85f:35139)
  • [8] G. Metivier, Interaction de chocs, Sem. Bony-Sjöstrand-Meyer (1984-1985). MR 819772 (87g:35152)
  • [9] -, Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d'espace, Trans. Amer. Math. Soc. 296 (1986), 431-479. MR 846593 (88a:35153)
  • [10] S. Alinhac, Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels (preprint).

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Article copyright: © Copyright 1989 American Mathematical Society

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