The Local Solutions Of A Class Of Nonlinear Wave Equations And Their Asymptotic Theory

This paper deals with the local solutions and asymptotic theory for initial value problems of a class of nonlinear wave equations.In Chapter 2, the local solutions of nonlinear wave equation )in high space dimensions is studied.It is proved that the Sobolev exponent of the equation is - Chapter 3establishes the asymptotic theory of initial value problems for a class of nonlinear wave equation in two space dimensions.The validity offormal approximations on a long time scale of order T = O(|e|-1) isdiscussed in the classical sense of C2JL .At the end of this chapter, anapplication of the asymptotic theory is given to a special perturbation wave equation in two space dimensions. Chapter 4 deals with the asymptotic theory of initial value problems for nonlinear wave equations in three space dimensions. The well-posedness and validation of formal approximations about time r = are discussed in the classical sense of C2. These results describe the validity of formal global solutions. At the end of this chapter, an application of the asymptotic theory is given to analyzing a special wave equation in three space dimensions.