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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The sharp form of Oleĭnik's entropy condition in several space variables


Author: David Hoff
Journal: Trans. Amer. Math. Soc. 276 (1983), 707-714
MSC: Primary 35L65
MathSciNet review: 688972
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Abstract: We investigate the conditions under which the Volpert-Kruzkov solution of a single conservation law in several space variables with flux $ F$ will satisfy the simplified entropy condition $ \operatorname{div}\,F^{\prime}(u) \leqslant 1/t$, and when this condition guarantees uniqueness for given $ {L^\infty}$ Cauchy data. We show that, when $ F$ is $ {C^1}$, our condition guarantees uniqueness iff $ F$ is isotropic, and that, for such $ F$, the Volpert-Kruzkov solution always satisfies our condition.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0688972-6
PII: S 0002-9947(1983)0688972-6
Article copyright: © Copyright 1983 American Mathematical Society