Pullback random attractors for fractional stochastic $ p $-Laplacian equation with delay and multiplicative noise

Xuping Zhang

doi:10.3934/dcdsb.2021107

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2022, Volume 27, Issue 3: 1695-1724. Doi: 10.3934/dcdsb.2021107

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Pullback random attractors for fractional stochastic $ p $-Laplacian equation with delay and multiplicative noise

Xuping Zhang

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

Received: January 2021

Early access: March 2021

Published: March 2022

This research was supported by Natural Science Foundation of Gansu Province (No. 20JR5RA522), Science Research Project for Colleges and Universities of Gansu Province (No. 2019B-047), Project of NWNU-LKQN2019-13 and Doctoral Research Fund of Northwest Normal University (No. 6014/0002020209)

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This paper is concerned with the pullback random attractors of nonautonomous nonlocal fractional stochastic $ p $-Laplacian equation with delay driven by multiplicative white noise defined on bounded domain. We first prove the existence of a continuous nonautonomous random dynamical system for the equations as well as the uniform estimates of solutions with respect to the delay time and noise. We then show pullback asymptotical compactness of solutions and the existence of tempered random attractors by utilizing the Arzela-Ascoli theorem and appropriate uniform estimates of the solutions. Finally, we establish the upper semicontinuity of the random attractors when time delay approaches zero.

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

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