Amplitude equation for SPDE with quadratic nonlinearities
- In this paper we rigorously derive stochastic amplitude equation for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we show that the solution of the original SPDE is approximated by the solution of the amplitude equation. Our results significantly improve older results. We focus on equations with quadratic nonlinearity and give applications to the one-dimensional Burgers equation and a model from surface growth.
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| Author: | Dirk BlömkerORCiDGND, Wael Wagih M. E. Elhaddad |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-10483 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1224 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2009-02) |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2009 |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | DFG |
| Release Date: | 2009/02/05 |
| Tag: | Amplitudengleichung; Mehrskalenansatz |
| GND-Keyword: | Stochastische partielle Differentialgleichung; Parabolische Differentialgleichung; Nichtlineare partielle Differentialgleichung |
| Note: | Erschienen in Electronic Journal of Probability, 14, S. 2527-2550, https://doi.org/10.1214/ejp.v14-716 |
| 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 |
