A Nekhoroshev Type Theorem For The Nonlinear Wave Equation In Gevrey Space

In this paper,we mainly study Nekhoroshev type theorem of the nonlinear wave equation utt = uxx-mu-f(u),x?[0,?],t?R at the origin on the finite x-interval[0,?]in Gevrey space.And it is divided into seven parts as following:In the first chapter,this section mainly firstly introduces the research status of infinite dimensional Hamiltonian system,then introduces study content and study results.In the second chapter,this section mainly studies the nonlinear wave equation as an infinite dimensional Hamiltonian system,and give some related definitions and proof of theorems.In the third chapter,this section mainly introduces the space of polynomial and some properties,and give two important lemmas and inequalities.In the fourth chapter,this section mainly introduces the nonresonance condition,which mainly estimates the measure of the smaller denominator produced by normal form.In the five chapter,this section mainly introduces the normal form.The content is divided into two parts,respectively recursive equation and normal form results.In the sex chapter,this section mainly introduces the proof of study result.In the seven chapter,this section mainly summarize the content of this paper.