Global Existence And Decay Rate Estimates For Two Lass Of Nonlinear Viscoelastic Equations With Coustic Boundary Conditions

Partial diferential equations was born in the early18th century, at that time,people dedicated to research how to create a partial diferential equation model orlook for some special equation solution or particular solution. By the19th century,with the rapid development of analysis, the research of partial diferential equationshas undergone a major change, many important equations, in particular, the nonlinearequation, to obtain the explicit solution is impossible. Therefore, the research of partialdiferential equations gradually transformed into study the posedness, that is the ex-istence, uniqueness and stability of solutions. For linear partial diferential equations,their existence and uniqueness and asymptotic have a lot of results. For the boundarydissipation problems of nonlinear wave equations have also been considered by manyscholars.This paper is studied to two class of nonlinear viscoelastic equations with acousticboundary conditions, using Galerkin method and energy method, we got some impor-tant results.The thesis is divided into three sections according to contents.Chapter1Introduction, we introduce the main contents of this paper.Chapter2In chapter2, we consider the boundary problem of nonlinear viscoelas-tic equationwhere γ>0, and g is a nonegative function. For certain initial data and suitable condi-tions on g and γ, we proved the solution is global and the energy decays exponentiallyor polynomially depending on the decay rate of the relaxation function g. Chapter3In chapter3, we consider the boundary problem of nonlinear viscoelas-tic equationwhere γ>0, ρ>0and g is a nonegative function. For certain initial data andsuitable conditions on g, ρ and γ, we proved the solution is global and the energydecays exponentially or polynomially depending on the decay rate of the relaxationfunction g.