Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (2): 203-213.

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Existence of Uniform Random Attractors for a Class of Delay Parabolic Equations

GONG Ting, LI Yayu, CHEN Guiling   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
  • Received:2022-06-11 Online:2023-03-26 Published:2023-03-26

Abstract: We considered the existence of uniform  random attractors for a class of delay parabolic equations with additive noise and non-autonomous external force terms on the smooth  bounded domains. Firstly, through the uniform estimation of the solution, we obtained  that the solution of the equation had a closed uniform pullback absorbing set with respect to the symbol space. Secondly, by Sobolev imbedding theorem and Arzela-Ascoli theorem,
the uniform pullback compactness of the solution was obtained.  Finally, the existence and uniqueness of uniform random attractor was proved.

Key words: uniform random attractor, delay, white noise, existence

CLC Number: 

  • O175.29