Semigroups Of Operators And Abstract Partial Differential Equations With Delay

This thesis is divided into three parts. In the first chapter, the one - to - one correspondence between mild solutions of an abstract deday equation and mild solutions of an associated abstract Cauchy problem is shown, and necessary and sufficient conditions for existence and uniqueness of mild solutions of the abstract delay equation are obtained. In the second chapter, the concept of an integrated abstract delay equation is introduced, and the equivalence of the well - posedness of an integrated delay equation and an associated integrated Cauchy problem is derived. In the third chapter, some results of inhomogeneous abstract delay equations are given.