Existence and upper semicontinuity of (L2, Lq) pullback attractors for a stochastic p-laplacian equation

Linfang Liu; Xianlong Fu

doi:10.3934/cpaa.2017023

Article Contents

2017, Volume 6: 443-474. Doi: 10.3934/cpaa.2017023

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Existence and upper semicontinuity of (L², L^q) pullback attractors for a stochastic p-laplacian equation

Linfang Liu and
Xianlong Fu^,

Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China

Author Bio: liulinfang1988@163.com (L. Liu)
xlfu@math.ecnu.edu.cn (X. Fu, the corresponding author)
xlfu@math.ecnu.edu.cn (X. Fu, the corresponding author)

Received: January 31, 2016

Revised: September 30, 2016

Published: August 2017

This research is supported by NSFof China (Nos. 11671142 and11371087), Science and Technology Commission of Shanghai Municipality (No. 13dz2260400) and Shanghai Leading Academic Discipline Project (No. B407), respectively

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Abstract

In this paper we study the dynamical behavior of solutions for a non-autonomous $p$-Laplacian equation driven by a white noise term. We first establish the abstract results on existence and continuity of bi-spatial pullback random attractors for a cocycle. Then by conducting some tail estimates and applying the obtained abstract results we show the existence and upper semi-continuity of $(L^{2}(\mathbb{R}^{n}), L^{q}(\mathbb{R}^{n}))$-pullback attractors for this $p$-Laplacian equation.

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Mathematics Subject Classification: 35B40, 35R60, 37L55, 60H15.

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