Acoustic Boundary Problem Of A Class Of Nonlinear Viscoelastic Wave Equation Is Studied

This paper is concerned with the existence, the exponential decay for the so-lution of the following nonlinear viscoelastic wave equation with acoustic bound-ary conditions,This dissertation is divided into four sections.In the first section, we introduce the importance and the international re-search progress of the nonlinear viscoelastic wave equation, we also state the hypotheses for the problem.In the second section, we list some preliminaries such as the Sobolev imbed-ding theorem, several kinds of important inequalities and so on.In the third section, we prove the existence of the solution to the problem (1.1)-(1.5). The proof of the existence includes Faedo-Galerkin approximation, some prior estimates, limiting process.In the forth section, we prove the exponential decay of the solution by im-plying the functional L(t):=ME(t)+mΨ(Υ)+ωΦ(t), where M,m,ω are positive constants, and the definitions of ψ(t),Φ(t) are given by...