Eventual norm continuity for neutral semigroups on Banach spaces

Abstract

In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.