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Scalar conservation laws with boundary conditions and rough data measure solutions
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2002 (English)In: Methods and Applications of Analysis, ISSN 1073-2772, E-ISSN 1945-0001, Vol. 9, no 4, 579-598 p.Article in journal (Refereed) Published
Abstract [en]

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

Place, publisher, year, edition, pages
2002. Vol. 9, no 4, 579-598 p.
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-90712OAI: oai:DiVA.org:kth-90712DiVA: diva2:506154
Note
NR 20140805Available from: 2012-02-27 Created: 2012-02-27 Last updated: 2017-12-07Bibliographically approved

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