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dc.contributor.authorSouganidis, Panagiotis E.
dc.contributor.authorPerthame, Benoît
dc.contributor.authorLions, Pierre-Louis
dc.subjectrough pathsen
dc.subjectdissipative solutionsen
dc.subjectkinetic formulationen
dc.subjectstochastic entropy conditionen
dc.subjectstochastic conservation lawsen
dc.subjectStochastic differential equationsen
dc.titleScalar conservation laws with rough (stochastic) fluxesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Mathematics [Chicago] University of Chicago;États-Unis
dc.contributor.editoruniversityotherBANG (INRIA Rocquencourt) INRIA – Laboratoire Jacques-Louis Lions;France
dc.contributor.editoruniversityotherLaboratoire Jacques-Louis Lions (LJLL) CNRS : UMR7598 – Université Pierre et Marie Curie (UPMC) - Paris VI;France
dc.description.abstractenWe develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear stochastic dependence. We introduce the notion of pathwise stochastic entropy solutions, which is closed with the local uniform limits of paths, and prove that it is well posed, i.e., we establish existence, uniqueness and continuous dependence, in the form of pathwise $L^1$-contraction, as well as some explicit estimates. Our approach is motivated by the theory of stochastic viscosity solutions, which was introduced and developed by two of the authors, to study fully nonlinear first- and second-order stochastic pde with multiplicative noise. This theory relies on special test functions constructed by inverting locally the flow of the stochastic characteristics. For conservation laws this is best implemented at the level of the kinetic formulation which we follow here.en
dc.relation.isversionofjnlnameStochastic Partial Differential Equations: Analysis and Computations
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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