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Regularity and backward compactness of attractors for non-autonomous lattice systems with random coefficients

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  • Wang, Renhai
  • Li, Yangrong

Abstract

We study longtime behavior for the non-autonomous lattice model with multiplicative white noise and a random coefficient in the discrete Laplace operator. We first show existence of a bi-spatial attractor when the initial space is the weighted square summation space and the terminal space is the weighted p-times summation space for p > 2. We then show backward compactness of the attractor in both initial and terminal spaces if the time-indexed forces are backward-tempered and backward-null. Finally, by proving identity of the attractors on the different universes of tempered or backward tempered sets, we show measurability of the attractor in the initial space and in the terminal space, respectively.

Suggested Citation

  • Wang, Renhai & Li, Yangrong, 2019. "Regularity and backward compactness of attractors for non-autonomous lattice systems with random coefficients," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 86-102.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:86-102
    DOI: 10.1016/j.amc.2019.02.036
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    References listed on IDEAS

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    1. Zhao, Wenqiang & Zhang, Yijin, 2016. "Compactness and attracting of random attractors for non-autonomous stochastic lattice dynamical systems in weighted space ℓρp," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 226-243.
    2. Cui, Hongyong & Li, Yangrong, 2015. "Existence and upper semicontinuity of random attractors for stochastic degenerate parabolic equations with multiplicative noises," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 777-789.
    3. Zhou, Shengfan & Tian, Yongxiao & Wang, Zhaojuan, 2016. "Fractal dimension of random attractors for stochastic non-autonomous reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 80-95.
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    Cited by:

    1. Yang, Shuang & Li, Yangrong, 2022. "Numerical attractors and approximations for stochastic or deterministic sine-Gordon lattice equations," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Li, Fuzhi & Xu, Dongmei, 2022. "Backward regularity of attractors for lattice FitzHugh-Nagumo system with double random coefficients," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Li, Yangrong & Wang, Fengling & Xia, Huan, 2024. "Continuity-sets of pullback random attractors for discrete porous media equations with colored noise," Applied Mathematics and Computation, Elsevier, vol. 465(C).

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