Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d’espace
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- Trans. Amer. Math. Soc. 296 (1986), 431-479 Request permission
Abstract:
The existence of shock front solutions to a system of conservation laws in several space variables has been proved by A. Majda, solving a Cauchy problem, with a suitable discontinuous Cauchy data. But, in general, the solution to such a Cauchy problem will present $N$ singularities, $N$ being the number of laws. In this paper we solve (locally) this Cauchy problem, with a Cauchy data which is piecewise smooth, in the case where all the singularities are expected to be shock waves. Actually the construction is written for a system of two laws, with two space variables and similarly, for such a system, the same method enables us to study the interaction of two shock waves. The key point, in the construction below, is the study of a nonlinear, free boundary Goursat problem.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 296 (1986), 431-479
- MSC: Primary 35L65; Secondary 76L05
- DOI: https://doi.org/10.1090/S0002-9947-1986-0846593-9
- MathSciNet review: 846593