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Compactness and attracting of random attractors for non-autonomous stochastic lattice dynamical systems in weighted space ℓρp

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  • Zhao, Wenqiang
  • Zhang, Yijin

Abstract

In this article, some sufficient conditions on the regularity of random attractors are first provided for general random dynamical systems in the weighted space ℓρp(p>2) of infinite sequences. They are then used to study the asymptotic dynamics of a class of non-autonomous stochastic lattice differential equations with spatially valued additive noises. The existences of tempered random attractors for this in both spaces ℓρ2 and ℓρp are proved respectively, which implies that the obtained ℓρ2-random attractor is compact and attracting in the topology of ℓρp space. To solve this, a common embedding space of ℓρ2 and ℓρp is constructed and some new estimates are also developed here.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:226-243
    DOI: 10.1016/j.amc.2016.06.045
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    References listed on IDEAS

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    1. 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.
    2. 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. Wang, Renhai & Wang, Bixiang, 2020. "Random dynamics of p-Laplacian lattice systems driven by infinite-dimensional nonlinear noise," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7431-7462.
    3. 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.

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