Exponential Stability Of Solutions For Two Classes Of Differential Variational Inequalities

In recent years,Differential Variational Inequalities(DVIs,for short)have become one of the most promising areas of applied mathematics.It combines various differential equations and variational inequalities to describe the dynamics of a system and its state variables over time.In the study of mechanics,economics,complementary system,optimization,optimal control and other fields,researchers usually use the theory of the differential variational inequalities to solve these practical problems.Most researchers are committed to studying the existence and uniqueness of the solution of the system and applying it to our life.In this thesis,we mainly study the existence,uniqueness,and exponential stability of solutions for two class of differential variational inequalities.And the full text is divided into five chapters:In chapter 1,we introduce the research background and research status of the existence,uniqueness and exponential stability of solutions of differential variational inequalities,then give the main methods and final results of this thesis.In chapter 2,we introduce the preliminary knowledge required in this thesis,including related definitions,lemmas,and theorems.In chapter 3,we consider the solution for a class of differential elliptic hemivariational inequalities.Firstly,we use the fixed point theorem and the related properties of operators to prove the existence and uniqueness of the solution of the system.Secondly,we obtain that the solution of the system is exponentially stableby by using the relevant conclusions of semigroup theory.Lastly,we given a corresponding example to illustrate the main research results of this chapter.In chapter 4,we consider the solution for a class of differential parabolic variational inequalities.Firstly,we use the Banach compression fixed point theorem,semigroup theory and the correlation properties of operators to prove the existence and uniqueness of the system solution.Secondly,by using the relevant conclusions of semigroup theory,we obtain that the solution of the system is exponentially stable.Finally,we give an example to illustrate the main research results of this chapter.In chapter 5,we summarize the entire content of this thesis and provide directions for future work.