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1997 Evolution semigroups for nonautonomous Cauchy problems
Gregor Nickel
Abstr. Appl. Anal. 2(1-2): 73-95 (1997). DOI: 10.1155/S1085337597000286


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.


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Gregor Nickel. "Evolution semigroups for nonautonomous Cauchy problems." Abstr. Appl. Anal. 2 (1-2) 73 - 95, 1997.


Published: 1997
First available in Project Euclid: 7 April 2003

zbMATH: 0938.47030
MathSciNet: MR1604240
Digital Object Identifier: 10.1155/S1085337597000286

Primary: 47D06
Secondary: 47A55

Keywords: evolution semigroup , nonautonomous abstract Cauchy problem , parabolic problems , Perturbation theory

Rights: Copyright © 1997 Hindawi

Vol.2 • No. 1-2 • 1997
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