Abstract

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP)  {u˙(t)=A(t)u(t)u(s)=x∈X on a Banach space X by the existence of certain evolution semigroups.Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “parabolic” case.