Coupling of scalar conservation laws in stratified porous media

Pages: 644 - 654, Issue Special, September 2007

 Abstract        Full Text (242.3K)              

Laurent Lévi - University of Pau & CNRS, Laboratory of Applied Mathematics, UMR 5142 CNRS, Batiment IPRA, B.P. 1155, 64013 PAU Cedex, France (email)
Julien Jimenez - Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques appliquées, UMR 5142, IPRA, BP 1155, 64013 Pau Cedex, France (email)

Abstract: 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.

Keywords:  Coupling of Parabolic-Hyperbolic Equations,Entropy formulation, Entropy Process Solution.
Mathematics Subject Classification:  35L65, 35K65.

Received: September 2006;      Revised: March 2007;      Published: September 2007.