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Counterexamples to the well posedness of the Cauchy problem for hyperbolic systems

hal.structure.identifierDipartimento di Matematica
dc.contributor.authorCOLOMBINI, F
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMÉTIVIER, Guy
dc.date.issued2015
dc.identifier.issn2157-5045
dc.description.abstractEnThis paper is concerned with the well posedness of the Cauchy problem for first order symmetric hyperbolic systems in the sense of Friedrichs. The classical theory says that if the coefficients of the system and if the coefficients of the symmetrizer are Lipschitz continuous, then the Cauchy problem is well posed in L 2. When the symmetrizer is Log-Lipschtiz or when the coefficients are analytic or quasi-analytic, the Cauchy problem is well posed C ∞. In this paper we give counterexamples which show that these results are sharp. We discuss both the smoothness of the symmetrizer and of the coefficients.
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.title.enCounterexamples to the well posedness of the Cauchy problem for hyperbolic systems
dc.typeArticle de revue
dc.identifier.doi10.2140/apde.2015.8.499
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalAnalysis & PDE
bordeaux.page499-511
bordeaux.volume8
bordeaux.peerReviewedoui
hal.identifierhal-01260615
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01260615v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Analysis%20&%20PDE&rft.date=2015&rft.volume=8&rft.spage=499-511&rft.epage=499-511&rft.eissn=2157-5045&rft.issn=2157-5045&rft.au=COLOMBINI,%20F&M%C3%89TIVIER,%20Guy&rft.genre=article


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