Quasi-Hyperbolicity and Delay Semigroups

Abstract

We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t)=Bu(t)+Φut, where ut is the history function and (B,D(B)) is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.