Modulation Equation for Stochastic Swift-Hohenberg Equation
- The purpose of this paper is to study the influence of large orunbounded domains on a stochastic PDE near a change of stability, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider the stochastic Swift-Hohenberg equation and derive rigorously the Ginzburg-Landau equation as a modulation equation for the amplitudes of the dominating modes. We verify that small global noise has the potential to stabilize the modulation equation, and thus to destroy the dominant pattern.
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| Author: | Dirk BlömkerORCiDGND, Wael W. MohammedGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-12492 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1567 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2011-14) |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2011 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2011/09/05 |
| Tag: | Swift-Hohenberg stochastic PDE; amplitude equations; Swift-Hohenberg; stabilisation |
| GND-Keyword: | Stochastische partielle Differentialgleichung; Partielle Differentialgleichung; Amplitudengleichung; Stabilisierung |
| Note: | Erschienen in SIAM Journal on Mathematical Analysis, 45, 1, S. 14-30, https://doi.org/10.1137/110846336 |
| 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): |  Deutsches Urheberrecht mit Print on Demand |
