Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equations

Li Song; Yangrong Li; Fengling Wang

doi:10.3934/eect.2022010

Article Contents

2022, Volume 11, Issue 6: 2033-2054. Doi: 10.3934/eect.2022010

This issue Previous Article Blow-up of solutions to a viscoelastic wave equation with nonlocal damping Next Article Pullback attractors for weak solution to modified Kelvin-Voigt model

Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equations

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author: liyr@swu.edu.cn (Yangrong Li)
^* Corresponding author: liyr@swu.edu.cn (Yangrong Li)

Received: October 2021

Revised: December 2021

Early access: February 2022

Published: December 2022

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Abstract

A non-autonomous random dynamical system is called to be controllable if there is a pullback random attractor (PRA) such that each fibre of the PRA converges upper semi-continuously to a nonempty compact set (called a controller) as the time-parameter goes to minus infinity, while the PRA is called to be asymptotically autonomous if there is a random attractor for another (autonomous) random dynamical system as a controller. We establish the criteria for ensuring the existence of the minimal controller and the asymptotic autonomy of a PRA respectively. The abstract results are illustrated in possibly non-autonomous stochastic p-Laplace lattice equations with tempered convergent external forces.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 37L55, 60H15.

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