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Modulation equation for SPDEs in unbounded domains with space–time white noise — Linear theory

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  • Bianchi, Luigi Amedeo
  • Blömker, Dirk

Abstract

We study the approximation of SPDEs on the whole real line near a change of stability via modulation or amplitude equations, which acts as a replacement for the lack of random invariant manifolds on extended domains. Due to the unboundedness of the underlying domain a whole band of infinitely many eigenfunctions changes stability. Thus we expect not only a slow motion in time, but also a slow spatial modulation of the dominant modes, which is described by the modulation equation.

Suggested Citation

  • Bianchi, Luigi Amedeo & Blömker, Dirk, 2016. "Modulation equation for SPDEs in unbounded domains with space–time white noise — Linear theory," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3171-3201.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:3171-3201
    DOI: 10.1016/j.spa.2016.04.024
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