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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Communicated by A. Kupiainen
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Blömker, D., Hairer, M. & Pavliotis, G. Modulation Equations: Stochastic Bifurcation in Large Domains. Commun. Math. Phys. 258, 479–512 (2005). https://doi.org/10.1007/s00220-005-1368-8
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DOI: https://doi.org/10.1007/s00220-005-1368-8