Existence in the large for Riemann problems for systems of conservation laws

Author:
Michael Sever

Journal:
Trans. Amer. Math. Soc. **292** (1985), 375-381

MSC:
Primary 35L65; Secondary 76N10

DOI:
https://doi.org/10.1090/S0002-9947-1985-0805969-5

MathSciNet review:
805969

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Abstract: An existence theorem in the large is obtained for the Riemann problem for nonlinear systems of conservation laws. Our principal assumptions are strict hyperbolicity, genuine nonlinearity in the strong sense, and the existence of a convex entropy function. The entropy inequality is used to obtain an a priori estimate of the strengths of the shocks and refraction waves forming a solution; existence of such a solution then follows by an application of finite-dimensional degree theory. The case of a single degenerate field is also included, with an additional assumption on the existence of Riemann invariants.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0805969-5

Keywords:
Conservation laws,
Riemann problems,
topological degree

Article copyright:
© Copyright 1985
American Mathematical Society