Journal of Guangxi Normal University(Natural Science Edition) ›› 2024, Vol. 42 ›› Issue (3): 151-158.doi: 10.16088/j.issn.1001-6600.2023061202

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Higher-order Stability of Attractors for Stochastic Reaction-Diffusion Equation

LI Zhi, ZHAO Wenqiang*   

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
  • Received:2023-06-12 Revised:2023-08-17 Online:2024-05-25 Published:2024-05-31

Abstract: The stability of random attractors of the stochastic reaction-diffusion equation with additive white noise is studied. First, with a general assumption on the nonlinear term, the solutions of the stochastic differential equation converge to the solutions of the deterministic equation in the initial space L2(RN), and the upper semi-continuity of the random attractors is obtained. In particular, by using the nonlinear decomposition and the difference estimation, we technically obtain the convergence of solutions and the upper semi-continuity of random attractors in Lp(RN)(p>2),where p is the growth index of the nonlinear function.

Key words: reaction-diffusion equation, random attractor, upper semi-continuity, addtitive noise, stability

CLC Number:  O192
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