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Cauchy problem for hyperbolic conservation laws with a relaxation term

Published online by Cambridge University Press:  14 November 2011

Christian Klingenberg  and
Yun-guang Lu
Christian Klingenberg
Affiliation:
Applied Mathematics Department, Heidelberg University, Heidelberg, Germany
Yun-guang Lu
Affiliation:
Young Scientist Lab of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, Wuhan, China
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Abstract

This paper considers the Cauchy problem for hyperbolic conservation laws arising in chromatography:

with bounded measurable initial data, where the relaxation term g(δ, u, v) converges to zero as the parameter δ > 0 tends to zero. We show that a solution of the equilibrium equation

is given by the limit of the solutions of the viscous approximation

of the original system as the dissipation ε and the relaxation δ go to zero related by δ = O(ε). The proof of convergence is obtained by a simplified method of compensated compactness [2], avoiding Young measures by using the weak continuity theorem (3.3) of two by two determinants.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 4 , 1996 , pp. 821 - 828
Copyright
Copyright © Royal Society of Edinburgh 1996

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