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Scalar conservation law with discontinuous flux in a bounded domain

Pages: 520 - 530, Issue Special, September 2007

 Abstract        Full Text (233.4K)              

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 consider the Dirichlet problem for a first-order hyperbolic equation with a convection term discontinuous with respect to the space variable. We introduce a definition of a weak entropy solution to the corresponding problem and then we prove existence and uniqueness of the entropy solution for a class of flux functions. The existence property is obtained by regularization of the flux function while for the uniqueness result we use the method of doubling variables and a Rankine-Hugoniot condition along the line of discontinuity.

Keywords:  Hyperbolic equation, entropy solution, discontinuous advection.
Mathematics Subject Classification:  Primary: 35L60, 35B05; Secondary: 35R05.

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