Scalar conservation law with discontinuous flux in a bounded domain

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2007, 2007(Special): 520-530. doi: 10.3934/proc.2007.2007.520

Scalar conservation law with discontinuous flux in a bounded domain

1.	Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques appliquées, UMR 5142, IPRA, BP 1155, 64013 Pau Cedex, France

Received September 2006 Revised March 2007 Published September 2007

Abstract
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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: discontinuous advection., entropy solution, Hyperbolic equation.

Mathematics Subject Classification: Primary: 35L60, 35B05; Secondary: 35R0.

Citation: Julien Jimenez. Scalar conservation law with discontinuous flux in a bounded domain. Conference Publications, 2007, 2007 (Special) : 520-530. doi: 10.3934/proc.2007.2007.520

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