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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Metadaten
Author:Dirk BlömkerORCiDGND, Wael Wagih M. E. Elhaddad
URN:urn:nbn:de:bvb:384-opus4-10483
Frontdoor URLhttps://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

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