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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMETIVIER, Guy
dc.date.accessioned2024-04-04T03:11:18Z
dc.date.available2024-04-04T03:11:18Z
dc.date.created2013-10-03
dc.date.issued2014
dc.identifier.issn2429-7100
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193765
dc.description.abstractEnThe Cauchy problem for first order system $L(t, x, \D_t, \D_x)$ is known to be well posed in $L^2$ when a it admits a microlocal symmetrizer $S(t,x, \xi)$ which is smooth in $\xi$ and Lipschitz continuous in $(t, x)$. This paper contains three main results. First we show that a Lipsshitz smoothness globally in $(t,x, \xi)$ is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is equivalent to the existence of \emph{full symmetrizers} having the same smoothness. This notion was first introduced in \cite{FriLa1}. This is the key point to prove the third result that the existence of microlocal symmetrizer is preserved if one changes the direction of time, implying local uniqueness and finite speed of propagation.
dc.language.isoen
dc.publisherÉcole polytechnique
dc.subject.enHyperbolic
dc.subject.ensystems of partial differential equations
dc.subject.ensymmerizers
dc.subject.enenergie estimate
dc.subject.enfinite speed of propgagation
dc.title.en$L^2$ well posed Cauchy Problems and Symmetrizability of First Order Systems
dc.typeArticle de revue
dc.identifier.doi10.5427/jep.2014
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv1310.4760
bordeaux.journalJournal de l'École polytechnique — Mathématiques
bordeaux.pagepp 39 -- 70
bordeaux.volume1
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00873785
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00873785v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20l'%C3%89cole%20polytechnique%20%E2%80%94%20Math%C3%A9matiques&rft.date=2014&rft.volume=1&rft.spage=pp%2039%20--%2070&rft.epage=pp%2039%20--%2070&rft.eissn=2429-7100&rft.issn=2429-7100&rft.au=METIVIER,%20Guy&rft.genre=article


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