UNSPECIFIED. (2003) Amplitude equations for locally cubic nonautonomous nonlinearities. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2 (3). pp. 464-486. ISSN 1536-0040

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Abstract

For systems of partial differential equations (PDEs) with locally cubic nonlinearities, which are perturbed by additive noise, we describe the essential dynamics for small solutions. If the system is near a change of stability, then a natural separation of time-scales occurs and the amplitudes of the dominant modes are given on a long time-scale by a stochastic ordinary differential equation. We consider applications to dynamic pitchfork bifurcation, pattern formation below the threshold of stability, and transient dynamics of stochastic PDEs near this deterministic bifurcations.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Publisher:	SIAM PUBLICATIONS
ISSN:	1536-0040
Date:	2003
Volume:	2
Number:	3
Number of Pages:	23
Page Range:	pp. 464-486
Identification Number:	10.1137/S1111111103421355
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/8535

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