# American Institute of Mathematical Sciences

2007, 2007(Special): 644-654. doi: 10.3934/proc.2007.2007.644

## Coupling of scalar conservation laws in stratified porous media

 1 University of Pau & CNRS, Laboratory of Applied Mathematics, UMR 5142 CNRS, Batiment IPRA, B.P. 1155, 64013 PAU Cedex, France 2 Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques appliquées, UMR 5142, IPRA, BP 1155, 64013 Pau Cedex

Received  September 2006 Revised  March 2007 Published  September 2007

We carry out the mathematical analysis of a quasilinear parabolic-hyperbolic problem in a multidimensional bounded domain $\Omega = \Omega_h \cup \Omega_p$, where $\Omega = \Omega \ \Omega_h$. We start by providing the definition of a weak solution $u$ through an entropy inequality on the whole $\Omega$ by using the classical Kuzhkov pairs. The uniqueness proof begins by focusing on the behavior of a weak solution in $\Omega_h$ and then in $\Omega_p$. The existence property uses a discontinuous vanishing viscosity method in accordance with the layer.
Citation: Laurent Lévi, Julien Jimenez. Coupling of scalar conservation laws in stratified porous media. Conference Publications, 2007, 2007 (Special) : 644-654. doi: 10.3934/proc.2007.2007.644
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