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
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2012-14)
Year of first Publication:2012
Publishing Institution:Universität Augsburg
Release Date:2012/11/22
amplitude equation; generalized Swift Hohenberg; additive noise; multiscale analysis
GND-Keyword:Stochastische partielle Differentialgleichung; Stochastische Analysis; Stochastische nichtlineare Differentialgleichung; Amplitudengleichung; Stabilität; Rauschen; Mehrskalenanalyse
Erschienen in Zeitschrift für angewandte Mathematik und Physik, 65, 6, S. 1107-1126,
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