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Fractal dimension of random attractors for stochastic non-autonomous reaction–diffusion equations

Author

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  • Zhou, Shengfan
  • Tian, Yongxiao
  • Wang, Zhaojuan

Abstract

In this paper, we first give some conditions for bounding the fractal dimension of a random invariant set for a non-autonomous random dynamical system on a separable Banach space. Then we apply these conditions to prove the finiteness of fractal dimension of the random attractors for stochastic reaction–diffusion equations with multiplicative white noise and additive white noise.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:80-95
    DOI: 10.1016/j.amc.2015.12.009
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    Cited by:

    1. Da, Nguyen Tien, 2023. "A new result on the fractal dimension estimates of random attractor for non-autonomous random 2D stochastic dynamical type systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Khalili Golmankhaneh, Alireza & Tejado, Inés & Sevli, Hamdullah & Valdés, Juan E. Nápoles, 2023. "On initial value problems of fractal delay equations," Applied Mathematics and Computation, Elsevier, vol. 449(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).
    4. 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.
    5. 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.

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