Probabilistic continuity of a pullback random attractor in time-sample

Shulin Wang; Yangrong Li

doi:10.3934/dcdsb.2020028

Article Contents

2020, Volume 25, Issue 7: 2699-2772. Doi: 10.3934/dcdsb.2020028

This issue Previous Article The existence and exponential behavior of solutions to time fractional stochastic delay evolution inclusions with nonlinear multiplicative noise and fractional noise Next Article Global solutions and random dynamical systems for rough evolution equations

Probabilistic continuity of a pullback random attractor in time-sample

Shulin Wang^1, and
Yangrong Li^2, ,

1.
Faculty of Eduction, Southwest University, Chongqing 400715, China
2.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author: Yangrong Li
^* Corresponding author: Yangrong Li

Received: February 28, 2019

Revised: July 31, 2019

Early access: April 2020

Published: July 2020

Li was supported by Natural Science Foundation of China grant 11571283, Wang was supported by National Social Science Foundation of China, 13th Five-year plan of Education grant BJA160059

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Abstract

Given a time-sample dependent attractor of a random dynamical system, we study its lower semi-continuity in probability along the time axis, and the criteria are established by using the local-sample asymptotically compactness for a triple-continuous system. The abstract results are applied to the non-autonomous stochastic p-Laplace equation on an unbounded domain with weakly dissipative nonlinearity. Without any additional hypotheses, we prove that the pullback random attractor is probabilistically continuous in both time and sample parameters.

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Mathematics Subject Classification: Primary: 37L55; Secondary: 35B41, 60H15.

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