The Decay Result Of Energy For The Solutions Of Viscoelastic Equations With Memory Kernel

In this paper,we study the decay result of the energy for the solution to a vis-coelastic equation with memory kernel and the decay result of the energy for the solution to a wave equation with delay term and viscoelastic term.This paper consists of four parts:In chapter one,we introduce the significance of viscoelastic wave equation and its main existing results.In chapter two,we introduce some definitions and inequalities which will be used in this paper.In chapter three,we study the fading behavior of energy for the solutions of viscoelastic system with non-dissipative memory kernel,by introducing suitable Lyapunov functionals and applying corresponding inequalities,we obtain the fading type of the viscoelas-tic equation.In chapter four,we study energy decay estimates of the solution for wave equation with variable coefficient delay term and viscoelastic term,we study the transmission problem of wave equations,we consider the wave propagations over material consisting of elastic and viscoelastic components.It is proved that under certain conditions,the exponential and poly-nomial types of decay are special cases.