Existence and uniqueness of the Riemann problem for a nonlinear system of conservation laws of mixed type

Authors:
L. Hsiao and P. de Mottoni

Journal:
Trans. Amer. Math. Soc. **322** (1990), 121-158

MSC:
Primary 35L65; Secondary 35M10

DOI:
https://doi.org/10.1090/S0002-9947-1990-0938919-3

MathSciNet review:
938919

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the system of conservation laws given by

The system is elliptic in the domain where and strictly hyperbolic when . We combine and generalize Lax criterion and Oleinik-Liu criterion to introduce the generalized entropy condition (G.E.C.) by which we can show that the Riemann problem always has a weak solution (any discontinuity satisfies the G.E.C.) for any initial data, however not necessarily unique. We introduce the minimum principle then in the definition of an admissible weak solution for the Riemann problem and the existence and uniqueness of the solution for any Riemann data.

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DOI:
https://doi.org/10.1090/S0002-9947-1990-0938919-3

Article copyright:
© Copyright 1990
American Mathematical Society