scholarly journals Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction–diffusion equations

2008 ◽  
Vol 245 (7) ◽  
pp. 1775-1800 ◽  
Author(s):  
Yangrong Li ◽  
Boling Guo
Keyword(s):  
Dynamical Systems ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Random Dynamical Systems ◽  
Diffusion Equations ◽  
Random Attractors ◽  
Stochastic Reaction

scholarly journals Random attractors for stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domains

2018 ◽  
Vol 16 (1) ◽  
pp. 862-884
Author(s):  
Xiaoyao Jia ◽  
Xiaoquan Ding ◽  
Juanjuan Gao
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Reaction Diffusion ◽  
Random Parameter ◽  
Reaction Diffusion Equations ◽  
Random Dynamical Systems ◽  
Diffusion Equations ◽  
Uhlenbeck Process ◽  
Random Attractors ◽  
Multiplicative White Noise

AbstractIn this paper we investigate the stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domain ℝn (n ≥ 2). We first transform the retarded reaction-diffusion equations into the deterministic reaction-diffusion equations with random parameter by Ornstein-Uhlenbeck process. Next, we show the original equations generate the random dynamical systems, and prove the existence of random attractors by conjugation relation between two random dynamical systems. In this process, we use the cut-off technique to obtain the pullback asymptotic compactness.

Attractors with higher-order regularity of stochastic reaction–diffusion equations on time-varying domains

2020 ◽  
Vol 20 (02) ◽  
pp. 2050041
Author(s):  
Lu Yang ◽  
Meihua Yang ◽  
Peter Kloeden
Keyword(s):  
Reaction Diffusion ◽  
Higher Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Initial Time ◽  
Regular Space ◽  
Time Varying ◽  
Regularity Properties ◽  
Random Attractors ◽  
Stochastic Reaction

Random attractors and their higher-order regularity properties are studied for stochastic reaction–diffusion equations on time-varying domains. Some new a priori estimates for the difference of solutions near the initial time and the continuous dependence in initial data in [Formula: see text] are proved. Then attraction of the random attractors in the higher integrability space [Formula: see text] for any [Formula: see text] and the regular space [Formula: see text] is established.

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