Electron. J. Diff. Equ., Vol. 2013 (2013), No. 191, pp. 1-25.

Asymptotic behavior of non-autonomous stochastic parabolic equations with nonlinear Laplacian principal part

Bixiang Wang, Boling Guo

We prove the existence and uniqueness of random attractors for the p-Laplace equation driven simultaneously by non-autonomous deterministic and stochastic forcing. The nonlinearity of the equation is allowed to have a polynomial growth rate of any order which may be greater than p. We further establish the upper semicontinuity of random attractors as the intensity of noise approaches zero. In addition, we show the pathwise periodicity of random attractors when all non-autonomous deterministic forcing terms are time periodic.

Submitted May 20, 2013. Published August 30, 2013.
Math Subject Classifications: 35B40, 35B41, 37L30.
Key Words: Pullback attractor; periodic random attractor; p-Laplace equation; upper semicontinuity.

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Bixiang Wang
Department of Mathematics
New Mexico Institute of Mining and Technology
Socorro, NM 87801, USA
email: bwang@nmt.edu
Boling Guo
Institute of Applied Physics and Computational Mathematics
P.O. Box 8009, Beijing 100088, China

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