Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 1, Number 4 (1996), 351-380.
Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations
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.
Abstr. Appl. Anal., Volume 1, Number 4 (1996), 351-380.
First available in Project Euclid: 7 April 2003
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34K30
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