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

Luigi Amedeo Bianchi and Dirk Blömker

Stochastic Processes and their Applications, 2016, vol. 126, issue 10, 3171-3201

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.

Keywords: Modulation equation; Amplitude equation; Unbounded domain; Random fields; Gaussian processes; Attractivity; Approximation; Linear theory; Stochastic convolution (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2016.04.024

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