Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem.
| 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 | |
| dc.date.accessioned | 2024-04-04T03:01:32Z | |
| dc.date.available | 2024-04-04T03:01:32Z | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 0219-8916 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192911 | |
| dc.description.abstractEn | The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an instantaneous response of the material, or by the Kerr-Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and two-dimensional transverse electric cases, the global existence of smooth solutions for the Kerr-Debye system is established. When the response time tends to zero, the convergence of the Kerr-Debye model to the Kerr model is established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr-Debye model. | |
| dc.language.iso | en | |
| dc.publisher | World Scientific Publishing | |
| dc.subject.en | relaxation | |
| dc.subject.en | nonlinear Maxwell equations | |
| dc.subject.en | Initial-boundary value problem | |
| dc.subject.en | Kerr model | |
| dc.subject.en | Kerr-Debye model | |
| dc.title.en | Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem. | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1142/S0219891609001939 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| bordeaux.journal | Journal of Hyperbolic Differential Equations | |
| bordeaux.page | 577-614 | |
| bordeaux.volume | 6 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00992606 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00992606v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Hyperbolic%20Differential%20Equations&rft.date=2009&rft.volume=6&rft.issue=3&rft.spage=577-614&rft.epage=577-614&rft.eissn=0219-8916&rft.issn=0219-8916&rft.au=CARBOU,%20Gilles&HANOUZET,%20Bernard&rft.genre=article |
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