Abstract:We consider the Cauchy problem for the (strictly hyperbolic, genuinely nonlinear) system of conservation laws with relaxationu Assume there exists an equilibrium curve_{t}- v_{x}= 0, v_{t}- s(u)_{x}= 1/h r(u,v).A(u), such thatr(u,A(u))=0. Under some assumptions onsandr, we prove the existence of global (in time) solutions of bounded variation,u, for^{h}, v^{h}h > 0fixed.As

h -> 0, we prove the convergence of a subsequence ofuto some^{h}, v^{h}u, vthat satisfy the equilibrium equationsu _{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, <debora@ares.mat.unimi.it>
- Graziano Guerra, <guerra@alpha.disat.unimi.it>
**Publishing information:****Comments:****Submitted by:**- <debora@ares.mat.unimi.it> September 22 1998.

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