Preprint 1998-036

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 u_t - v_x = 0,     v_t - 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, u^h, v^h, for h > 0 fixed.

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

u_t - A(u)_x = 0,     v(t, � ) = A(u(t, � ))     \forall t \geq 0.

Paper:

Available as PostScript.

Title:

Global BV solutions and relaxation limit for a system of conservation

Author(s):

Debora Amadori, mailto:debora@ares.mat.unimi.it

Graziano Guerra, mailto:guerra@alpha.disat.unimi.it

Publishing information:

Comments:

Submitted by:

mailto:debora@ares.mat.unimi.it September 22 1998.