Abstract:

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 L^p (p[gteq]2) decay rate.

Key words: Hyperbolic systems with relaxation, global smoothly solution, rarefaction waves, decay estimate