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Random dynamics of p-Laplacian lattice systems driven by infinite-dimensional nonlinear noise

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  • Wang, Renhai
  • Wang, Bixiang

Abstract

This article is concerned with the global existence and random dynamics of the non-autonomous p-Laplacian lattice system defined on the entire integer set driven by infinite-dimensional nonlinear noise. The existence and uniqueness of mean square solutions to the equations are proved when the nonlinear drift and diffusion terms are locally Lipschitz continuous. It is shown that the mean random dynamical system generated by the solution operators has a unique tempered weak pullback random attractor in a Bochner space. The existence of invariant measures for the stochastic equations in the space of square summable sequences is also established. The idea of uniform tail-estimates of solutions is employed to show the tightness of a family of distribution laws of the solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7431-7462
    DOI: 10.1016/j.spa.2020.08.002
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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.
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