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Continuity-sets of pullback random attractors for discrete porous media equations with colored noise

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  • Li, Yangrong
  • Wang, Fengling
  • Xia, Huan

Abstract

For a random non-autonomous porous media lattice system driven by nonlinear colored noise, we prove the unique existence and local compactness of a pullback random attractor. We then mainly study the continuity-set (the set of all points of continuity) of the pullback random attractor on the time-sample plane with respect to the Hausdorff metric. With some calculations, we find that the continuity-set has four geometrical numerical features:

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:465:y:2024:i:c:s0096300323006033
    DOI: 10.1016/j.amc.2023.128434
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    References listed on IDEAS

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    1. Ma, Qiaozhen & Xu, Ling, 2017. "Random attractors for the coupled suspension bridge equations with white noises," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 38-48.
    2. 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.
    3. 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).
    4. 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).
    5. 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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