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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d'espace


Author: Guy Métivier
Journal: Trans. Amer. Math. Soc. 296 (1986), 431-479
MSC: Primary 35L65; Secondary 76L05
MathSciNet review: 846593
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0846593-9
PII: S 0002-9947(1986)0846593-9
Article copyright: © Copyright 1986 American Mathematical Society