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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
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

Abstract

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
Copyright
Copyright © Royal Society of Edinburgh 2001

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