ABSTRACT
In this chapter, we present a systematic semigroup approach to linear partial differential equations with delay.
In Section 3.1, we associate an operator (A,D(A)) on the Banach space X × Lp([−1, 0],X) to the abstract delay equation on a Banach space X. There is a one-to-one correspondence between the solutions of the abstract delay equation and the solutions of the abstract Cauchy problem corresponding to the associated operator A (see Theorem 3.12). Thus the question of well-posedness of the delay equation reduces to the question of whether or not the operator (A,D(A)) generates a strongly continuous semigroup.
