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Note on strongly hyperbolic systems with involutive characteristics
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | MÉTIVIER, Guy | |
hal.structure.identifier | Department of Information and Computer Sciences [Toyonaka] | |
dc.contributor.author | NISHITANI, Tatsuo | |
dc.date.accessioned | 2024-04-04T03:11:38Z | |
dc.date.available | 2024-04-04T03:11:38Z | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193792 | |
dc.description.abstractEn | We 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.iso | en | |
dc.title.en | Note on strongly hyperbolic systems with involutive characteristics | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-01444389 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-01444389v1 | |
bordeaux.COinS | ctx_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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