Existence, stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations

In this paper, we study the existence, stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise. We first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structu...

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Bibliographic Details
Published in:Nonlinear analysis 2014-07, Vol.103, p.9-25
Main Author: Wang, Bixiang
Format: Article
Language:English
Subjects:
Bifurcation
Bifurcations
Mathematical analysis
Noise
Nonlinearity
Periodic attractor
Random attractor
Random complete solution
Random periodic solution
Stability
Stochasticity
Uniqueness
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Summary:In this paper, we study the existence, stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise. We first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions. We then examine the existence and stability of random complete quasi-solutions and establish the relations of these solutions and the structures of tempered attractors. When the stochastic equations are incorporated with periodic forcing, we obtain the existence and stability of random periodic solutions. For the stochastic Chafee–Infante equation, we further establish the multiplicity and stochastic bifurcation of complete and periodic solutions.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2014.02.013