Abstract and Applied Analysis
Volume 2 (1997), Issue 1-2, Pages 73-95
doi:10.1155/S1085337597000286
Evolution semigroups for nonautonomous Cauchy problems
Arbeitsbereich Funktionalanalysis, Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, Tübingen D - 7 207, Germany
Received 14 October 1996
Copyright © 1997 Gregor Nickel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.