Existence And Uniqueness Of Global Solution For A Class Of Wave Equation With Viscoelastic Term

In this thesis,we discuss the existence and uniqueness of solution for a class of wave equation with viscoelastic term and nonlinear Neumann boundary dissipation.At first we will establish the existence and uniqueness of solution on a finite time interval by using the theory of maximal monotone operator theory.Then by using the energy estimation of solution to get the global solution.The first chapter briefly introduces the development process of viscoelastic equations and the existing research results on the existence and uniqueness of solutions containing viscoelastic terms.The second chapter briefly introduces the relevant function spaces,related theorems,basic inequalities,and monotone operator theory in the article.The third chapter uses the maximal monotone operator theory to prove that there is a unique solution to the equation in a finite time region firstly.As usual,using energy functional estimation,the global solution of the equation exists.