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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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