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Kinetic decomposition for the generalized BBM–Burgers equations with dissipative term

Published online by Cambridge University Press:  12 July 2007

Seok Hwang
Seok Hwang
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA (seokhwan@math.usc.edu)
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Abstract

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We consider the generalized Benjamin–Bona–Mahony–Burgers (BBM–Burgers) equations with dissipative term. We establish the condition under which the solutions uα,β,γ converge in a strong topology to the entropy solution of a scalar conservation laws using methodology developed by Hwang and Tzavaras. First, we obtain the approximate transport equation for the given BBM–Burgers equations. Then, using the averaging lemma, we obtain the convergence.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 6 , December 2004 , pp. 1149 - 1162
Copyright
Copyright © Royal Society of Edinburgh 2004