Abstract and Applied Analysis
Volume 2 (1997), Issue 1-2, Pages 73-95

Evolution semigroups for nonautonomous Cauchy problems

Gregor Nickel

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.


In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP){u˙(t)=A(t)u(t)u(s)=xX 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.