On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
| hal.structure.identifier | Dipartimento di Matematica | |
| dc.contributor.author | COLOMBINI, Ferruccio | |
| hal.structure.identifier | Dipartimento di Matematica e Geoscienze [Trieste] | |
| dc.contributor.author | SANTO, Daniele | |
| hal.structure.identifier | Université de Lyon | |
| dc.contributor.author | FANELLI, Francesco | |
| 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/20.500.12278/193790 | |
| dc.description.abstractEn | The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H ∞ , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evident a priori in our setting, due to the very low regularity of coefficients and solutions. 2010 Mathematics Subject Classification: 35L45 (primary); 35B45, 35B65 (secondary). | |
| dc.language.iso | en | |
| dc.subject.en | hyperbolic system | |
| dc.subject.en | microlocal symmetrizability | |
| dc.subject.en | log-Lipschitz regularity | |
| dc.subject.en | loss of derivatives | |
| dc.subject.en | global and local Cauchy problem | |
| dc.subject.en | well-posedness | |
| dc.title.en | On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients | |
| 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-01444452 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01444452v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=COLOMBINI,%20Ferruccio&SANTO,%20Daniele&FANELLI,%20Francesco&M%C3%89TIVIER,%20Guy&rft.genre=preprint |
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