Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation
| Autor: | Bernard Hanouzet, Roberto Natalini, Gilles Carbou |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Appliquées de Bordeaux (MAB), Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1, Istituto per le Applicazioni del Calcolo 'Mauro Picone' (IAC), Consiglio Nazionale delle Ricerche [Roma] (CNR), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), istituto per le applicazioni del calculo (IAC), Consiglio Nazionale delle Ricerche (CNR) |
| Rok vydání: | 2009 |
| Předmět: |
Pointwise
Semilinear behavior Isentropic process Applied Mathematics 010102 general mathematics Mathematical analysis Degenerate energy levels Nonlinear optics 01 natural sciences Infimum and supremum Hyperbolic systems Suliciu model 010101 applied mathematics Numerical approximation Relaxation systems Kerr-Debye model Dissipative hyperbolic systems [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Relaxation (approximation) 0101 mathematics Analysis Mathematics Kerr–Debye model Linear degeneration |
| Zdroj: | Journal of Differential Equations Journal of Differential Equations, Elsevier, 2009, 246, pp.291-319 Journal of Differential Equations, Elsevier, 2009, 246 (1), pp.291--319 Journal of differential equations 246 (2009): 291–319. doi:10.1016/j.jde.2008.05.015 info:cnr-pdr/source/autori:Carbou G.; Hanouzet B.; Natalini R./titolo:Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation/doi:10.1016%2Fj.jde.2008.05.015/rivista:Journal of differential equations (Print)/anno:2009/pagina_da:291/pagina_a:319/intervallo_pagine:291–319/volume:246 (2008). info:cnr-pdr/source/autori:Carbou G., Hanouzet B., Natalini R./titolo:Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation/doi:/rivista:Journal of differential equations (Print)/anno:2008/pagina_da:/pagina_a:/intervallo_pagine:/volume |
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2008.05.015 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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