Existence And Regularity Of Solutions Of Nonlocal Cauchy Problem For Two Kinds Of Neutral Evolution Equations

Neutral differential evolution equations are an important type of evolution equations,having a wide applied background in many subjects.Existence and regularity of solutions for this kind of equations are of great important theoretical value and application signifi-cance.In this thesis we mainly apply theory of analytic semigroup,fractional powers and fixed point theorem to study the existence and regularity of the solutions for two types of neutral evolution equations with non-local conditions.The whole thesis contains three chapters.In Chapter 1,we gave a brief outline of the research background related to this thesis and the main work of this dissertation.In Chapter 2,we consider a class of neutral partial functional differential equation with state dependent non-local conditions.First,using analytic semigroups theory and Banach fixed point theorem we proved that the equation has strict solutions.Then,its solutions belong to C^?-continuous under appropriate conditions are also discussed here.Finally three examples are presented to illustrate the obtained results.The objective of Chapter 3 is to study a class of neutral functional differential evolution equations with nonlocal conditions defined on infinite interval.It is assumed that the operator semigroup(T(t))_t?0generated by the linear part of the equation is exponentially stable.First,the equation has global mild solutions are proved by using Sadovskii's fixed point theorem.Then,we study the existence of global strict solutions for the considered equation and sufficient conditions for this are obtained.In addition,global asymptotic stability of strict solutions are also discussed.