| Title:
|
Stability in nonlinear evolution problems by means of fixed point theorems (English) |
| Author:
|
Koliha, J. J. |
| Author:
|
Straškraba, Ivan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
37-59 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value problem for a parabolic equation in several space variables. (English) |
| Keyword:
|
evolution equations |
| Keyword:
|
stabilization of solutions |
| Keyword:
|
parabolic problem |
| MSC:
|
34C30 |
| MSC:
|
34D15 |
| MSC:
|
34G20 |
| MSC:
|
35B40 |
| MSC:
|
35K20 |
| MSC:
|
35K99 |
| MSC:
|
47H20 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0891.34065 |
| idMR:
|
MR1455469 |
| . |
| Date available:
|
2009-01-08T18:29:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118901 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[11] Rauch J.: Stability of motion for semilinear equations.in: Boundary Value Problems for Linear Evolution Partial Differential Equations, Proceedings of the NATO Advanced Study Institute held in Liège, Belgium, September 6-17, 1976, H. G. Garnir (ed.), NATO Advanced Study Institute Series C, Mathematical and Physical Sciences, vol. 29, Reidel Publishing Co., Dordrecht, 1977. Zbl 0347.35015, MR 0492677 |
| Reference:
|
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| . |
