HAL : hal-00589587, version 1
 Applied Mathematics Research eXpress (2012) 2 (2012), 127-151.
 General fractal conservation laws arising from a model of detonations in gases
 (2012)
 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.
 1 : Institut de Mathématiques et de Modélisation de Montpellier (I3M) CNRS : UMR5149 – Université Montpellier II - Sciences et techniques
 Domaine : Mathématiques/Equations aux dérivées partielles
Liste des fichiers attachés à ce document :
 PDF
 general-fractal.pdf(284.1 KB)
 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