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.
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| Author: | Bernd AulbachGND, Nguyen Van Minh |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-295524 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/29552 |
| ISSN: | 1687-0409OPAC |
| Parent Title (English): | Abstract and Applied Analysis |
| Publisher: | Hindawi |
| Place of publication: | Akron, OH |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 1996 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2017/07/21 |
| Volume: | 1 |
| First Page: | 351 |
| Last Page: | 380 |
| DOI: | https://doi.org/10.1155/S108533759600019X |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 3.0: Creative Commons - Namensnennung (mit Print on Demand) |
