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Modulation Equations: Stochastic Bifurcation in Large Domains

D. Blömker·M. Hairer·G. A. Pavliotis
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Abstract

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations.

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D. Blömker, M. Hairer, G. A. Pavliotis. 2004-08-10. Modulation Equations: Stochastic Bifurcation in Large Domains. https://doi.org/10.1007/s00220-005-1368-8

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