Approximate Controllability Of Two Kinds Of Non-autonomous Evolution Systems With Nonlocal Conditions

Non-autonomous differential evolution equations are an important kind of evolution equations,which have wide application backgrounds in many fields.Research on control problems of this kind of equations has very important theoretical and application value.In this thesis,we mainly apply theories of linear evolution operators,fractional power operators and resolvent operators,theory of measure integrals and fixed-point principle to study the approximate controllability of two kinds of non-autonomous evolution systems with nonlocal conditions.The results obtained here develop and generalize the existing work in related papers.The full text is divided into three chapters.The first chapter mainly introduces the relevant research background and briefly summarizes the main work of this dissertation.In Chapter 2,we study the approximate controllability of a kind of non-autonomous evolution equations with state-dependent nonlocal conditions.Firstly,the existence of mild solutions for the system is discussed by using theory of linear evolution operators and Schauder’s fixed point theorem.Based on this,the approximate controllability of the system is discussed under the resolvent operator condition and sufficient conditions for the approximate controllability is established.In the end,an application example is given.In Chapter 3,we consider the approximate controllability of a kind of semilinear non-autonomous measure differential equations with nonlocal conditions.Based on the relevant theories of Lebesgue-Stieltjes integrals,regular functions,and linear evolution operators,the existence and uniqueness of solutions of the considered system are discussed by using Schauder’s fixed point theorem,and sufficient conditions for approximate controllability of the system are established successfully.