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dc.contributor.authorAlibaud, Nathaël
HAL ID: 5327
dc.contributor.authorKarch, Grzegorz
dc.contributor.authorImbert, Cyril
HAL ID: 9368
ORCID: 0000-0002-1290-8257
dc.date.accessioned2010-02-09T13:33:37Z
dc.date.available2010-02-09T13:33:37Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3359
dc.language.isoenen
dc.subjectAsymptotic behavior of solutionsen
dc.subjectFractal Burgers equationen
dc.subjectEntropy solutionsen
dc.subjectSelf-similar solutionsen
dc.subject.ddc519en
dc.titleAsymptotic properties of entropy solutions to fractal Burgers equationen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherInstytut Matematyczny Uniwersytet Wroclawski;Pologne
dc.contributor.editoruniversityotherUniversité de Franche-Comté;France
dc.description.abstractenWe study properties of solutions of the initial value problem for the nonlinear and nonlocal equation ut+(−∂2 x)α/2u+uux = 0 with α ∈ (0, 1], supplemented with an initial datum approaching the constant states u± (u− <u+) as x → ±∞, respectively. It was shown by Karch, Miao & Xu (SIAM J. Math. Anal. 39 (2008), 1536--1549) that, for α ∈ (1, 2), the large time asymptotics of solutions is described by rarefaction waves. The goal of this paper is to show that the asymptotic profile of solutions changes for α ≤ 1. If α = 1, there exists a self-similar solution to the equation which describes the large time asymptotics of other solutions. In the case α ∈ (0, 1), we show that the nonlinearity of the equation is negligible in the large time asymptotic expansion of solutions.en
dc.relation.isversionofjnlnameSIAM Journal of Mathematical Analysis
dc.relation.isversionofjnlvol42
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages354-376
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/090753449
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00369449/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAM
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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