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

DOI:
https://doi.org/10.1090/S0002-9939-03-06961-2

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 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

Email:
milisic@math.u-bordeaux.fr, vuk.milisic@epfl.ch

DOI:
https://doi.org/10.1090/S0002-9939-03-06961-2

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