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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.

References [Enhancements On Off] (What's this?)

  • [1] Michael Crandall and Andrew Majda, The method of fractional steps for conservation laws, Numer. Math. 34 (1980), 258-314. MR 571291 (81j:65101)
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  • [4] A. I. Volpert, The spaces $ BV$ and quasilinear equations, Math. USSR-Sb. 2 (1967), 225-267. MR 0216338 (35:7172)

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