THE ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR SEMILINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

摘要

This paper deals with the asymptotic theory of initial value problems for semilinear wave equations in three space dimensions. The well-posedness and validity of formal approximations on a long time scale of order │ε│~-1 are discussed in the classical sense of C~2. This result describes accu- ratively the approximations of ,solutions. At the end of this paper, an application of the asymptotic theory is given to analyze a special model for a perturbed wave equation.