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Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws
Author(s):
Vuk
Milisic
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1727-1737.
MSC (2000):
Primary 35L65;
Secondary 35B25
Posted:
January 17, 2003
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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:
10.1090/S0002-9939-03-06961-2
PII:
S 0002-9939(03)06961-2
Keywords:
Scalar conservation law,
boundary condition,
kinetic approximation,
$BV$ estimates,
entropy solution
Received by editor(s):
July 22, 2001
Posted:
January 17, 2003
Communicated by:
Suncica Canic
Copyright of article:
Copyright
2003,
American Mathematical Society
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