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

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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  • 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.

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


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