Some Results On Hyperbolic System With Relaxation

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).