Abstract and Applied Analysis

Evolution semigroups for nonautonomous Cauchy problems

Gregor Nickel

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2, Number 1-2 (1997), 73-95.

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049737244

Digital Object Identifier
doi:10.1155/S1085337597000286

Mathematical Reviews number (MathSciNet)
MR1604240

Zentralblatt MATH identifier
0938.47030

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

Keywords
Evolution semigroup nonautonomous abstract Cauchy problem perturbation theory parabolic problems

Citation

Nickel, Gregor. Evolution semigroups for nonautonomous Cauchy problems. Abstr. Appl. Anal. 2 (1997), no. 1-2, 73--95. doi:10.1155/S1085337597000286. https://projecteuclid.org/euclid.aaa/1049737244


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