Abstract and Applied Analysis
Volume 2 (1997), Issue 1-2, Pages 73-95
doi:10.1155/S1085337597000286
Evolution semigroups for nonautonomous Cauchy problems
Gregor Nickel
Arbeitsbereich Funktionalanalysis, Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, Tübingen D - 7 207, Germany
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.