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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Multiple viscous solutions for systems of conservation laws
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by A. V. Azevedo and D. Marchesin PDF
Trans. Amer. Math. Soc. 347 (1995), 3061-3077 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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