The attractors for 2nd-order stochastic delay lattice systems
Stationary and time-periodic patterns of two-predator and one-prey systems with prey-taxis
Random attractor for stochastic non-autonomous damped wave equation with critical exponent
Zhaojuan Wang 1, and Shengfan Zhou 2,,
School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, China
Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China
*Corresponding author: Shengfan Zhou
Received April 2016 Revised July 2016 Published November 2016
Fund Project: The authors is supported by NSFC grant No. 11471290,61271396,11326114,11401244. Zhejiang Natural Science Foundation grant No. LY14A010012 and Zhejiang Normal University Foundation grant No. ZC304014012.
In this paper, we prove the existence of random attractor and obtainan upper bound of fractal dimension of random attractor forstochastic non-autonomous damped wave equation with criticalexponent and additive white noise. We first prove the existence of arandom attractor by carefully splitting the positivity of the linearoperator in the corresponding random evolution equation of the firstorder in time and by carefully decomposing the solutions of systemthrough two different modes, and we show the boundedness of randomattractor in a higher regular space by a recurrence method. Then weestablish a criterion to bound the fractal dimension of a randominvariant set for a cocycle and applied these conditions to get anupper bound of fractal dimension of the random attractor ofconsidered system.
Keywords: Stochastic damped wave equation, random attractor, fractal dimension, critical exponent.
Mathematics Subject Classification: Primary:37L55;Secondary:35B41, 35B4.
Citation: Zhaojuan Wang, Shengfan Zhou. Random attractor for stochastic non-autonomous damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 545-573. doi: 10.3934/dcds.2017022
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Zhaojuan Wang Shengfan Zhou