Abstract and Applied Analysis

Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations

Bernd Aulbach and Nguyen Van Minh

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Abstract

This paper is concerned with the existence and stability of solutions of a class of semilinear nonautonomous evolution equations. A procedure is discussed which associates to each nonautonomous equation the so-called evolution semigroup of (possibly nonlinear) operators. Sufficient conditions for the existence and stability of solutions and the existence of periodic oscillations are given in terms of the accretiveness of the corresponding infinitesimal generator. Furthermore, through the existence of integral manifolds for abstract evolutionary processes we obtain a reduction principle for stability questions of mild solutions. The results are applied to a class of partial functional differential equations.

Article information

Source
Abstr. Appl. Anal., Volume 1, Number 4 (1996), 351-380.

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049726080

Digital Object Identifier
doi:10.1155/S108533759600019X

Mathematical Reviews number (MathSciNet)
MR1481548

Zentralblatt MATH identifier
0934.34051

Subjects
Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34K30
Secondary: 47H20

Keywords
Evolutionary process evolution semigroup semilinear nonautonomous equation nonlinear semigroup stability periodic solution accretive operator integral manifold instability

Citation

Aulbach, Bernd; Minh, Nguyen Van. Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations. Abstr. Appl. Anal. 1 (1996), no. 4, 351--380. doi:10.1155/S108533759600019X. https://projecteuclid.org/euclid.aaa/1049726080


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