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Modulation Equations: Stochastic Bifurcation in Large Domains

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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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Authors and Affiliations

  1. Institut für Mathematik, RWTH Aachen, Templergraben 55, 52052, Aachen, Germany

    D. Blömker

  2. Dept. of Mathematics, The University of Warwick,  

    M. Hairer & G. A. Pavliotis

  3. Dept. of Mathematics, Imperial College, London

    G. A. Pavliotis

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  1. D. Blömker
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  2. M. Hairer
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  3. G. A. Pavliotis
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Correspondence to D. Blömker.

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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

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