A front-tracking alternative to the random choice method

Author:
Nils Henrik Risebro

Journal:
Proc. Amer. Math. Soc. **117** (1993), 1125-1139

MSC:
Primary 35L65; Secondary 76L05, 76M99

DOI:
https://doi.org/10.1090/S0002-9939-1993-1120511-X

MathSciNet review:
1120511

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Abstract: An alternative to Glimm's proof of the existence of solutions to systems of hyperbolic conservation laws is presented. The proof is based on an idea by Dafermos for the single conservation law and in some respects simplifies Glimm's original argument. The proof is based on construction of approximate solutions of which a subsequence converges. It is shown that the constructed solution satisfies Lax's entropy inequalities. The construction also gives a numerical method for solving such systems.

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1120511-X

Article copyright:
© Copyright 1993
American Mathematical Society