Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Debora Amadoria1 and Graziano Guerraa2

a1 Dipartimento di Matematica, Università degli Studi di Milano, via Saldini, 50–20133 Milano, Italy

a2 Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, 20126 Milano, Italy

Abstract

We consider the Cauchy problem for the (strictly hyperbolic, genuinely nonlinear) system of conservation laws with relaxation

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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

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(Received April 28 1999)

(Accepted July 13 1999)