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A Bhatnagar–Gross–Krook approximation to scalar conservation laws with discontinuous flux

Published online by Cambridge University Press:  01 October 2010

F. Berthelin  and
J. Vovelle
F. Berthelin
Affiliation:
Laboratoire J. A. Dieudonné, UMR 6621 CNRS, Université de Nice, Parc Valrose, 06108 Nice Cedex 2, France ([email protected])
J. Vovelle
Affiliation:
Institut Camille Jordan, UMR 5218 CNRS, Université Claude Bernard Lyon 1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France ([email protected])
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Abstract

We study the Bhatnagar–Gross–Krook (BGK) approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy problem for the BGK approximation is well posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 5 , October 2010 , pp. 953 - 972
Copyright
Copyright © Royal Society of Edinburgh 2010

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