Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays

2016 ◽  
Vol 16 (05) ◽  
pp. 1750001 ◽  
Author(s):  
Jingyu Wang ◽  
Yejuan Wang ◽  
Dun Zhao
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Random Dynamical Systems ◽  
Degenerate Parabolic Equations ◽  
Pullback Attractors ◽  
Asymptotic Compactness ◽  
Unbounded Delay ◽  
Bounded Set ◽  
Degenerate Parabolic ◽  
Linear Degenerate

The theory of pullback attractors for multi-valued non-compact random dynamical systems and a method of asymptotic compactness based on the concepts of the Kuratowski measure of the non-compactness of a bounded set are used to prove the existence of pullback attractors for the multi-valued non-compact random dynamical systems associated with the semi-linear degenerate parabolic unbounded delay equations with both deterministic and random external terms.

Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains

2020 ◽  
pp. 2150033
Author(s):  
Fahe Miao ◽  
Hui Liu ◽  
Jie Xin
Keyword(s):  
White Noise ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Stationary Process ◽  
Unbounded Domains ◽  
Degenerate Parabolic Equations ◽  
Pullback Attractors ◽  
Multiplicative White Noise ◽  
Degenerate Parabolic

The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations of stochastic degenerate parabolic equations. We then prove that the attractors of Wong–Zakai approximations converge to the attractor of stochastic degenerate parabolic equations driven by multiplicative white noise.

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