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AMPLITUDE EQUATIONS FOR SPDES: APPROXIMATE CENTRE MANIFOLDS AND INVARIANT MEASURES

By Dirk Bl, Ömker and Martin Hairer

Abstract

Abstract. We review recent results on the approximation of transient dynamics of SPDEs by amplitude equations. As an application we derive the flow along an approximate centre manifold, and we study the dynamics of random fixed points. To discuss the long-time behaviour we give an approximation result for invariant measures. Key words. Amplitude equation, SPDE, separation of time scales, approximate centre manifold, bifurcation, multiple scale analysis, invariant measures AMS(MOS) subject classifications. 60H10, 60H15

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.332.1236
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