Existence and Approximation of Manifolds for the Swift-Hohenberg Equation with a Parameter-Reference-Cited by-同舟云学术

Existence and Approximation of Manifolds for the Swift-Hohenberg Equation with a Parameter

Published:2018-07-12 Issue: Volume:2018 Page:1-6
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Guo Yanfeng¹²^ORCID,Guo Chunxiao³^ORCID,Li Donglong¹

Affiliation:

1. School of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China

2. School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China

3. Department of Mathematics, China University of Mining and Technology Beijing 100083, China

Abstract

The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modeling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2018/1423170.pdf

Reference24 articles.

1. Qualitative Properties of Local Random Invariant Manifolds for SPDEs with Quadratic Nonlinearity

2. Geometric shape of invariant manifolds for a class of stochastic partial differential equations

3. Approximation of Stochastic Invariant Manifolds