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Global BV solutions and relaxation limit for a system of conservation laws

Published online by Cambridge University Press:  11 July 2007

Debora Amadori  and
Graziano Guerra
Debora Amadori
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, via Saldini, 50–20133 Milano, Italy
Graziano Guerra
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, 20126 Milano, Italy
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Abstract

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We consider the Cauchy problem for the (strictly hyperbolic, genuinely nonlinear) system of conservation laws with relaxation Assume there exists an equilibrium curve A(u), such that r(u,A(u)) = 0. Under some assumptions on σ and r, we prove the existence of global (in time) solutions of bounded variation, uε, υε, for ε > 0 fixed.

As ε → 0, we prove the convergence of a subsequence of uε, υε to some u, υ that satisfy the equilibrium equations

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 1 , February 2001 , pp. 1 - 26
Copyright
Copyright © Royal Society of Edinburgh 2001