UPPER SEMICONTINUITY OF UNIFORM RANDOM ATTRACTORS FOR DELAY PARABOLIC EQUATION

Ting Gong; Zhe Pu; Dingshi Li

doi:10.11948/20220239

2023 Volume 13 Issue 2

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Ting Gong, Zhe Pu, Dingshi Li. UPPER SEMICONTINUITY OF UNIFORM RANDOM ATTRACTORS FOR DELAY PARABOLIC EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 928-953. doi: 10.11948/20220239

Citation:

Ting Gong, Zhe Pu, Dingshi Li. UPPER SEMICONTINUITY OF UNIFORM RANDOM ATTRACTORS FOR DELAY PARABOLIC EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 928-953. doi: 10.11948/20220239

UPPER SEMICONTINUITY OF UNIFORM RANDOM ATTRACTORS FOR DELAY PARABOLIC EQUATION

1.
School of Mathematics, Southwest Jiaotong University, 610031, Chengdu, China

Corresponding author: Email: zhepuws@my.swjtu.edu.cn(Z. Pu)
Fund Project: The authors were supported by NSFC (11971394), Central Government Funds for Guiding Local Scientific and Technological Development (2021ZYD0010) and Fundamental Research Funds for the Central Universities (2682021ZTPY057)

Abstract

Abstract

This paper concentrates on the upper semicontinuity of uniform random attractors for a class of delay parabolic equations with additive noise and nonautonomous external force terms. Firstly, through the uniform estimation of the solution, it is proved that the solution of the equation has a closed uniform pullback absorbing set with respect to the symbolic space. Then, by Arzela-Ascoli theorem, we prove uniformly pullback compactness of solutions as well as the existence and uniqueness of uniform random attractors. Finally, we prove the upper semicontinuity of the uniform random attractors when time delay approaches to zero.
- Uniform random attractor /
- delay /
- upper semicontinuity
MSC: 35B40, 35B41, 37L30

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References

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