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| HAL : hal-00589587, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Applied Mathematics Research eXpress (2012) 2 (2012), 127-151. |
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| General fractal conservation laws arising from a model of detonations in gases |
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| Matthieu Alfaro 1Jerome Droniou 1 |
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| (2012) |
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| We consider a model of cellular detonations in gases. They consist in conservation laws with a non-local pseudo-differential operator whose symbol is asymptotically $|\xi|^\lam$, where $0<\lam \leq 2$; it can be decomposed as the $\lambda /2$ fractional power of the Laplacian plus a convolution term. After defining the notion of entropy solution, we prove the well-posedness in the $L^\infty$ framework. In the case where $1<\lam \leq2$ we also prove a regularizing effect. In Appendix, we show that the assumptions made to perform the mathematical study are satisfied by the considered physical model of detonations. |
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| 1 : | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et techniques |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| hal-00589587, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00589587 | |
| oai:hal.archives-ouvertes.fr:hal-00589587 | |
| Contributeur : Matthieu Alfaro | |
| Soumis le : Vendredi 29 Avril 2011, 13:37:48 | |
| Dernière modification le : Mardi 5 Février 2013, 15:18:02 | |
