Some Remarks on Stabilization by Additive Noise
- We review some results on stabilization of solutions to semilinear parabolic PDEs near a change of stability due to additive degenerate noise. Our analysis is based on the rigorous derivation of a stochastic amplitude equation for the dominant mode and on careful estimates on its solution. Furthermore, a few numerical examples which corroborate our theoretical findings are presented.
| Author: | Dirk BlömkerORCiDGND, Martin Hairer, Grigorios A. Pavliotis |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-10171 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1179 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2008-29) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2008/10/13 |
| Year of first Publication: | 2008 |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | University of Warwick, Imperial College London |
| Release Date: | 2008/10/13 |
| Tag: | Mehrskalenansatz; Stabilität |
| GND-Keyword: | Stochastische nichtlineare Differentialgleichung; Stochastische parabolische Differentialgleichung; Burgers-Gleichung; Amplitudengleichung |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
