Multiple viscous solutions for systems of conservation laws

Authors:
A. V. Azevedo and D. Marchesin

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3061-3077

MSC:
Primary 35L65; Secondary 35M10, 76L05

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277093-8

MathSciNet review:
1277093

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Abstract: We exhibit an example of mechanism responsible for multiple solutions in the Riemann problem for a mixed elliptic-hyperbolic type system of two quadratic polynomial conservation laws. In this example, multiple solutions result from folds in the set of Riemann solutions. The multiple solutions occur despite the fact that they all satisfy the viscous profile entropy criterion. The failure of this criterion to provide uniqueness is evidence in support of a need for conceptual change in the theory of shock waves for a system of conservation laws.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1277093-8

Article copyright:
© Copyright 1995
American Mathematical Society