Upper semi-continuity of non-autonomous fractional stochastic $ p $-Laplacian equation driven by additive noise on $ \mathbb{R}^n $

Xiaohui Zhang; Xuping Zhang

doi:10.3934/dcdsb.2022081

Article Contents

2023, Volume 28, Issue 1: 385-407. Doi: 10.3934/dcdsb.2022081

This issue Previous Article Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases Next Article Hopf bifurcation for a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge

Upper semi-continuity of non-autonomous fractional stochastic $ p $-Laplacian equation driven by additive noise on $ \mathbb{R}^n $

Xiaohui Zhang and
Xuping Zhang^,

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

^*Corresponding author: Xuping Zhang
^*Corresponding author: Xuping Zhang

Received: January 31, 2022

Early access: May 2022

Published: January 2023

This work was supported by the Outstanding Youth Science Fund of Gansu Province (No. 21JR7RA159), the Natural Science Foundations of Gansu Province (20JR5RA522) and Project of NWNU-LKQN2019-13

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Abstract

This paper deals with the asymptotic behavior of the solutions to a class of non-autonomous fractional stochastic $ p $-Laplacian equation driven by linear additive noise on the entire space $ \mathbb{R}^n $. We firstly prove the existence of a continuous non-autonomous cocycle for the equation as well as the uniform estimates of solutions. We then show pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractors and the uniform tail-estimates of the solutions for large space variables when time is large enough to surmount the lack of compact Sobolev embeddings on unbounded domains. Finally, we establish the upper semi-continuity of the random attractors when noise intensity approaches zero.

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Mathematics Subject Classification: Primary 35B40; Secondary 35B41, 37L30.

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