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Note on strongly hyperbolic systems with involutive characteristics

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMÉTIVIER, Guy
hal.structure.identifierDepartment of Information and Computer Sciences [Toyonaka]
dc.contributor.authorNISHITANI, Tatsuo
dc.date.accessioned2024-04-04T03:11:38Z
dc.date.available2024-04-04T03:11:38Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193792
dc.description.abstractEnWe consider the Cauchy problem in L 2 for first order system. A necessary condition is that the system must be uniformly diagonaliz-able, or equivalently that it admits a bounded symmetrizer. A sufficient condition is that it admits a smooth (Lipschtitz) symmetrizer, which is true when the system is hyperbolic, diagonalizable with eigen-values of constant multiplicities. Counterexamples show that uniform diagonalizability is not sufficient in general for systems with variable coefficients and indicate that the symplectic properties of the set Σ of the singular points of the characteristic variety are important. In this paper, give a new class of systems for which the Cauchy problem is well posed in L 2. The main assumption is that Σ is a smooth involutive manifold and the system is transversally strictly hyperbolic.
dc.language.isoen
dc.title.enNote on strongly hyperbolic systems with involutive characteristics
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01444389
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01444389v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=M%C3%89TIVIER,%20Guy&NISHITANI,%20Tatsuo&rft.genre=preprint


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