Semilinear Behavior for Totally Linearly Degenerate Hyperbolic Systems with Relaxation
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CARBOU, Gilles | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HANOUZET, Bernard | |
| hal.structure.identifier | istituto per le applicazioni del calculo [IAC] | |
| dc.contributor.author | NATALINI, Roberto | |
| dc.date.accessioned | 2024-04-04T02:53:13Z | |
| dc.date.available | 2024-04-04T02:53:13Z | |
| dc.date.created | 2008 | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192153 | |
| dc.description.abstractEn | We investigate totally linearly degenerate hyperbolic systems with relaxation. We aim to study their semilinear behavior, which means that the local smooth solutions cannot develop shocks, and the global existence is controlled by the supremum bound of the solution. In this paper we study two specific examples: the {\it Suliciu}-type and the {\it Kerr-Debye}-type models. For the Suliciu model, which arises from the numerical approximation of isentropic flows, the semilinear behavior is obtained using pointwise estimates of the gradient. For the Kerr-Debye systems, which arise in nonlinear optics, we show the semilinear behavior via energy methods. For the original Kerr-Debye model, thanks to the special form of the interaction terms, we can show the global existence of smooth solutions. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Semilinear Behavior for Totally Linearly Degenerate Hyperbolic Systems with Relaxation | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal of Differential Equations | |
| bordeaux.page | 291--319 | |
| bordeaux.volume | 246 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00281547 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00281547v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2009&rft.volume=246&rft.issue=1&rft.spage=291--319&rft.epage=291--319&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=CARBOU,%20Gilles&HANOUZET,%20Bernard&NATALINI,%20Roberto&rft.genre=article |
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