Multi-Scale Analysis of SPDEs with Degenerate Additive Noise

  • We consider a quite general class of SPDEs with quadratic and cubic nonlinearities and derive rigorously amplitude equations, using the natural separation of time-scales near a change of stability. We show that degenerate additive noise has the potential to stabilize or destabilize the dynamics of the dominant modes, due to additional deterministic terms arising in averaging. We focus on equations with quadratic and cubic nonlinearities and give applications to the Burgers' equation, the Ginzburg-Landau equation and generalized Swift-Hohenberg equation.

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Author:Wael W. MohammedGND, Dirk BlömkerORCiDGND, Konrad Klepel
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-06)
Year of first Publication:2013
Publishing Institution:Universität Augsburg
Release Date:2013/04/05
GND-Keyword:Amplitudengleichung; Mehrskalenanalyse; Stochastische nichtlineare Differentialgleichung; Stochastische parabolische Differentialgleichung
Erschienen in Journal of Evolution Equations, 14, 2, S. 273-298,
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