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Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy

hal.structure.identifieristituto per le applicazioni del calculo [IAC]
dc.contributor.authorBIANCHINI, Stefano
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHANOUZET, Bernard
hal.structure.identifieristituto per le applicazioni del calculo [IAC]
dc.contributor.authorNATALINI, Roberto
dc.date.accessioned2024-04-04T02:53:13Z
dc.date.available2024-04-04T02:53:13Z
dc.date.created2006
dc.date.issued2007
dc.identifier.issn0010-3640
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192151
dc.description.abstractEnWe study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. We show that these solutions approach constant equilibrium state in the Lp-norm at a rate O(t^(-m/2(1-1/p))), as t tends to $\infty$, for p in [min ( m,2),+ \infty]. Moreover, we can show that we can approximate, with a faster order of convergence, theconservative part of the solution in terms of the linearized hyperbolic operator for m >= 2, and by a parabolic equation in the spirit of Chapman-Enskog expansion. The main tool is given by a detailed analysis of the Green function for the linearized problem.
dc.language.isoen
dc.publisherWiley
dc.title.enAsymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv0805.3614
bordeaux.journalCommunications on Pure and Applied Mathematics
bordeaux.page1559-1622
bordeaux.volume60
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue11
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00281551
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00281551v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20on%20Pure%20and%20Applied%20Mathematics&rft.date=2007&rft.volume=60&rft.issue=11&rft.spage=1559-1622&rft.epage=1559-1622&rft.eissn=0010-3640&rft.issn=0010-3640&rft.au=BIANCHINI,%20Stefano&HANOUZET,%20Bernard&NATALINI,%20Roberto&rft.genre=article


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