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

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