Modulation Equations: Stochastic Bifurcation in Large Domains |
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| Authors: | Email author" target="_blank">D?Bl?mkerEmail author M?Hairer G A?Pavliotis |
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| Institution: | (1) Institut für Mathematik, RWTH Aachen, Templergraben 55, 52052 Aachen, Germany;(2) Dept. of Mathematics, The University of Warwick,;(3) Dept. of Mathematics, Imperial College, London |
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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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