Evolution semigroups for nonautonomous Cauchy problems

Abstract

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems urn:x-wiley:10853375:media:aaa632147:aaa632147-math-0001 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.