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Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures

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Probability and Partial Differential Equations in Modern Applied Mathematics

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 140))

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.

The work of the first author was supported by DFG “Forschungsst ipendium” grant BL 535/5-1. He would like to thank the IMA for support.

The work of the second author was supported by the Fonds National Suisse.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, RWTH Aachen, D-52056, Aachen, Germany

    Dirk Blömker

  2. MRC, University of Warwick, UK

    Martin Hairer

Authors
  1. Dirk Blömker
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  2. Martin Hairer
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Oregon State University, Covallis, OR, 97331, USA

    Edward C. Waymire

  2. Department of Applied Mathematics, Illionis Institute of Technology, Chicago, IL, 60616, USA

    Jinqiao Duan

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Blömker, D., Hairer, M. (2005). Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures. In: Waymire, E.C., Duan, J. (eds) Probability and Partial Differential Equations in Modern Applied Mathematics. The IMA Volumes in Mathematics and its Applications, vol 140. Springer, New York, NY. https://doi.org/10.1007/978-0-387-29371-4_4

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