Amplitude Equations for SPDEs with Cubic Nonlinearities

  • For a quite general class of SPDEs with cubic nonlinearities we derive igorously amplitude equations describing the essential dynamics using the natural separation of time-scales near a change of stability. Typical examples are the Swift-Hohenberg equation, the Ginzburg-Landau (or Allen-Cahn) equation and some model from surface growth. We discuss the impact of degenerate noise on the dominant behavior, and see that additive noise has the potential to stabilize the dynamics of the dominant modes. Furthermore, we discuss higher order corrections to the amplitude equation.

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Author:Dirk BlömkerORCiDGND, Wael W. MohammedGND
Frontdoor URL
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-18)
Year of first Publication:2010
Publishing Institution:Universität Augsburg
Release Date:2010/12/07
GND-Keyword:Stochastische nichtlineare Differentialgleichung; Stochastische parabolische Differentialgleichung
Erschienen in Stochastics, 85, 2, S. 181-215,
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