The Initial Boundry Value Problem Of A Class Of Nonlinear Wave Equations

This paper study initial boundry value problem for a class of nonlinear dispersive-dissipative wave equations. Existence of the global solution is proved tinder some restictions on the nonlinear term. the whole paper is arranged as follows: In chapter 1, we will introduce some phiycal background of this equation, at the same time, we will survey some results available so far.In chapter 2, we collect some basic material which be used in the next chapters. Such as Sobolev space, imbedding theorems and so on.In chapter 3, we study this nonlinear wave equation with the first boundary conditions. and the existence of the global solution is proved by the means of the Galerkin method.In the chapter 4, we study this nonlinear wave equation with the third boundary conditions. and the existence of the global solution is proved.In the last chapter, we give a conclusion of this paper.