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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 3, pp 1353–1372 | Cite as

Stochastic Swift-Hohenberg Equation with Degenerate Linear Multiplicative Noise

  • Marco Hernández
  • Kiah Wah Ong
Article

Abstract

We study the dynamic transition of the Swift-Hohenberg equation (SHE) when linear multiplicative noise acting on a finite set of modes of the dominant linear flow is introduced. Existence of a stochastic flow and a local stochastic invariant manifold for this stochastic form of SHE are both addressed in this work. We show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation, and obtain numerical evidence suggesting that this picture is a good approximation for the full system as well.

Keywords

Swift-Hohenberg equation driven by multiplicative noise Model reduction Stochastic bifurcation 

Mathematics Subject Classification

35R60 34F05 37D10 37L10 60H15 

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Notes

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA

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