Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation

Yanfeng  Guo; Jinqiao Duan; Donglong  Li

doi:10.3934/dcdss.2016071

Article Contents

2016, Volume 9, Issue 6: 1701-1715. Doi: 10.3934/dcdss.2016071

This issue Previous Article Global existence and uniqueness of the solution for the fractional Schrödinger-KdV-Burgers system Next Article Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum

Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation

1.
School of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006
2.
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received: May 31, 2015

Revised: August 31, 2016

Published: November 2016

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Abstract

Random invariant manifolds are considered for a stochastic Swift-Hohenberg equation with multiplicative noise in the Stratonovich sense. Using a stochastic transformation and a technique of cut-off function, existence of random invariant manifolds and attracting property of the corresponding random dynamical system are obtained by Lyaponov-Perron method. Then in the sense of large probability, an approximation of invariant manifolds has been investigated and this is further used to describe the geometric shape of the invariant manifolds.

Keywords:

Stochastic partial differential equations,
random invariant manifolds,
approximation of invariant manifolds,
stochastic transformation,
Lyaponov-Perron method.

Mathematics Subject Classification: Primary: 60H15, 37H05; Secondary: 37L55, 37L25.

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