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Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws

Author: Vuk Milisic
Journal: Proc. Amer. Math. Soc. 131 (2003), 1727-1737
MSC (2000): Primary 35L65; Secondary 35B25
Published electronically: January 17, 2003
MathSciNet review: 1955259
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Abstract: We present some new convergence results for a discrete velocities BGK approximation to an initial boundary value problem for a single hyperbolic conservation law. In this paper we show stability and convergence toward a unique entropy solution in the general $BV$ framework without any restriction either on the data of the limit problem or on the set of velocity of the BGK model.

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Additional Information

Vuk Milisic
Affiliation: Mathématiques Appliquées de Bordeaux UMR(54 66), Université Bordeaux 1, 351 cours de la Libération, F-33405 Talence, France

Keywords: Scalar conservation law, boundary condition, kinetic approximation, $BV$ estimates, entropy solution
Received by editor(s): July 22, 2001
Published electronically: January 17, 2003
Communicated by: Suncica Canic
Article copyright: © Copyright 2003 American Mathematical Society