SOME RESULTS ON HYPERBOLIC SYSTEMS WITH RELAXATION*

In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they prove that the global smooth solutions of the hyperbolic conservation laws systems with relaxation converge to rarefaction waves solution at a determined Lp(p ≥ 2) decay rate.