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December 2002 Scalar Conservation Laws with Boundary Conditions and Rough Data Measure Solutions
Bachir Ben Moussa, Anders Szepessy
Methods Appl. Anal. 9(4): 579-598 (December 2002).

Abstract

Uniqueness and existence of $L^$#x221E;$ solutions to initial boundary value problems for scalar conservation laws, with continuous flux functions, is derived by $L^1$ contraction of Young measure solutions. The classical Kruzkov entropies, extended in Bardos, LeRoux and Nedelec’s sense to boundary value problems, are sufficient for the contraction. The uniqueness proof uses the essence of Kruzkov’s idea with his symmetric entropy and entropy flux functions, but the usual doubling of variables technique is replaced by the simpler fact that mollified measure solutions are in fact smooth solutions. The mollified measures turn out to have not only weak but also strong boundary entropy flux traces. Another advantage with the Young measure analysis is that the usual assumption of Lipschitz continuous flux functions can be relaxed to continuous fluxes, with little additional work.

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Bachir Ben Moussa. Anders Szepessy. "Scalar Conservation Laws with Boundary Conditions and Rough Data Measure Solutions." Methods Appl. Anal. 9 (4) 579 - 598, December 2002.

Information

Published: December 2002
First available in Project Euclid: 1 September 2009

zbMATH: 1166.35349
MathSciNet: MR2006606

Rights: Copyright © 2002 International Press of Boston

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Vol.9 • No. 4 • December 2002
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