The Cauchy problem for weakly hyperbolic systems
| hal.structure.identifier | Dipartimento di Matematica | |
| dc.contributor.author | COLOMBINI, F | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MÉTIVIER, Guy | |
| dc.date.accessioned | 2024-04-04T03:11:37Z | |
| dc.date.available | 2024-04-04T03:11:37Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193791 | |
| dc.description.abstractEn | We consider the well-posedness of the Cauchy problem in Gevrey spaces for N × N first order weakly hyperbolic systems. The question is to know wether the general results of M.D.Bronštein [Br] and K.Kajitani [Ka2] can be improved when the coefficients depend only on time and are smooth, as it has been done for the scalar wave equation in [CJS]. The anwser is no for general systems, and yes when the system is uniformly diagonalizable: in this case we show that the Cauchy problem is well posed in all Gevrey classes G s when the coefficients are C ∞. Moreover, for 2 × 2 systems and some other special cases, we prove that the Cauchy problem is well posed in G s for s < 1 + k when the coefficients are C k , which is sharp following the counterexamples of S.Tarama [Ta1]. The main new ingredient is the construction, for all hyperbolic matrix A, of a family of approximate symmetrizers, S ε , the coefficients of which are polynomials of ε and the coefficients of A and A *. MSC Classification : 35 L 50, 35 L 45, 35 L 40. | |
| dc.language.iso | en | |
| dc.subject.en | hyperbolic systems | |
| dc.subject.en | Cauchy problem | |
| dc.subject.en | symmetrizers | |
| dc.subject.en | well posed- ness | |
| dc.subject.en | Gevrey spaces | |
| dc.title.en | The Cauchy problem for weakly hyperbolic systems | |
| 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-01444446 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01444446v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=COLOMBINI,%20F&M%C3%89TIVIER,%20Guy&rft.genre=preprint |
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