Nonlinear Viscoelastic Wave Equation Existence And Asymptotic Behavior

This paper is concerned with the existence, the uniqueness and the exponen-tial decay for the solution of the following nonlinear viscoelastic wave equation with Dirichlet boundary conditionThis 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 and the uniqueness of the solution to the problem (1.1)-(1.3). The proof of the existence includes Faedo-Galerkin approximation, some prior estimates, limiting process and contraction mapping principle.In the forth section, we prove the exponential decay of the solution by defin-ing the function where we can prove that there existΤ1> 0,κ≥0, for(?)t≥1/η, energy function E(t) satisfying...