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March 2017, 6(2): 443-474. doi: 10.3934/cpaa.2017023
Existence and upper semicontinuity of (L2, Lq) 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
xlfu@math.ecnu.edu.cn (X. Fu, the corresponding author)
Received February 2016 Revised October 2016 Published January 2017
Fund Project: 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.
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.
Keywords: Stochastic p-Laplacian equation, bi-spatial pullback attractor, upper semi-continuity, omega-compactness.
Mathematics Subject Classification: 35B40, 35R60, 37L55, 60H15.
Citation: Linfang Liu, Xianlong Fu. Existence and upper semicontinuity of (L2, Lq) pullback attractors for a stochastic p-laplacian equation. Communications on Pure & Applied Analysis, 2017, 6 (2) : 443-474. doi: 10.3934/cpaa.2017023
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Linfang Liu Xianlong Fu