Quasi-Hyperbolicity and Delay Semigroups

Abstract

We study quasi-hyperbolicity of the delay semigroup associated with the equation $u^{\mathrm{\prime }}(t)=Bu(t)+\mathrm{\Phi }{u}_t$, where $u_t$ 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.