| The hyperbolic conservation laws with relaxation appear in many physical systems such as nonequilibrium gas dynamics, flood flow with friction, magnetohydrodynamics, etc. Firstly, the thesis proves that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws system with relaxation; secondly, in the large time station, the thesis proves that the global smooth solutions of the hyperbolic conservation laws system with relaxation converge to rarefaction waves solution at a determined L(p> 2) decay rate.In Chapter 1, the thesis studys the following Cauthy problem to hyperbolic system with nonlinear relaxation termwe prove that for the initial value with bounded C1 norm, there exists a unique global smooth solution for the Cauthy problem(1),(2);In Chapter 2, the thesis considers the following hyperbolic system with relaxation termand the sclar conservaton law equationwhen e is fixed, for a certain class of initial data , in the large time station, the thesis gets a determined Lp(p >2) decay rate between the golbal smooth solutions of system (3) and the rarefaction waves solution of equation (4). |
