Amplitude Equation for the Generalized Swift Hohenberg Equation With Noise
- We derive an amplitude equation for a stochastic partial differential equation (SPDE) of Swift-Hohenberg type with a nonlinearity that is composed of a stable cubic and an unstable quadratic term, under the assumption that the noise acts only on the constant mode. Due to the natural separation of time-scales, solutions are approximated well by the slow modes. Nevertheless, via the nonlinearity, the noise gets transmitted to those modes too, such that multiplicative noise appears in the amplitude equation.
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| Author: | Konrad Klepel, Dirk BlömkerORCiDGND, Wael W. MohammedGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-21301 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2130 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2012-14) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2012/11/22 |
| Year of first Publication: | 2012 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2012/11/22 |
| Tag: | Swift-Hohenberg-Gleichung additive noise; amplitude equation; generalized Swift Hohenberg; multiscale analysis |
| GND-Keyword: | Stochastische partielle Differentialgleichung; Stochastische Analysis; Stochastische nichtlineare Differentialgleichung; Amplitudengleichung; Stabilität; Rauschen; Mehrskalenanalyse |
| Note: | Erschienen in Zeitschrift für angewandte Mathematik und Physik, 65, 6, S. 1107-1126, https://doi.org/10.1007/s00033-013-0371-8 |
| 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 |
