Preprint 1998-036

Global BV Solutions and Relaxation Limit for a System of Conservation Laws

Debora Amadori and Graziano Guerra

Abstract: We consider the Cauchy problem for the (strictly hyperbolic, genuinely nonlinear) system of conservation laws with relaxation
ut - vx = 0,     vt - s(u)x = 1/h r(u,v).
Assume there exists an equilibrium curve A(u), such that r(u,A(u))=0. Under some assumptions on s and r, we prove the existence of global (in time) solutions of bounded variation, uh, vh, for h > 0 fixed.

As h -> 0, we prove the convergence of a subsequence of uh, vh to some u, v that satisfy the equilibrium equations

ut - A(u)x = 0,     v(t, · ) = A(u(t, · ))     \forall t \geq 0.

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Global BV solutions and relaxation limit for a system of conservation
Debora Amadori, <>
Graziano Guerra, <>
Publishing information:
Submitted by:
<> September 22 1998.

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