General fractal conservation laws arising from a model of detonations in gases

Matthieu Alfaro (1) , Jerome Droniou (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro, Jerome Droniou. General fractal conservation laws arising from a model of detonations in gases. Applied Mathematics Research eXpress, 2012, 2012 (2), pp.127-151. ⟨10.1093/amrx/abr015⟩. ⟨hal-00589587⟩