Mixed Initial-boundary Value Problem For Quasilinear Hyperbolic System

There have existed many good results of the Cauchy problem for quasilin-ear hyperbolic systems with inner dissipative terms and the mixed initial-boundary valve problem without inner dissipative terms,but the joint problems combining inner dissipation with boundary dissipation are completely unkown.The present PH.D thesis deals with the mixed initial-boundary value problem for quasilinear hy-perbolic systems with some inner dissipation and boundary dissipation.The author proves the global existence and uniqueness of the classical solutions to the mixed initial-boundary value problem and the solutions decay exponentially. Then,the author gives some examples to illustrate.Providing weaker assumptions,the author also proves the global existence and uniqueness of the classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems in a half-unbounded domain and the solutions decay polynomially.The arrangement of the thesis is as follows:In chapter l,the author gives a brief introduction to dissipation,and then present our questions and main results.In chapter 2,the author cites the theory and the main results of the cauchy problem for quasilinear hyperbolic systems with inner dissipative terms and the mixed initial-boundary value problem for quasilinear hyperbolic systems without inner terms.In chapter 3,by means of integrating along the characteristic curve,the author deals with the mixed initial-boundary value problem for quasilinear hyperbolic sys-tems with inner dissipation and boundary dissipation.The results are proved in this chapter.Then,the author gives a comparison with the results mentioned in chapter 2 and some examples to illustrate our results.In chapter 4,the author deals with the mixed initial-boundary value problem for quasilinear hyperbolic systems with some kind of inner dissipation in a half-unbounded domain.The results are proved in this chapter.At the same time,the author gives a brief comparison with our results in chapter 3.