Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 191, pp. 1-25.
Title: Asymptotic behavior of non-autonomous stochastic parabolic
equations with nonlinear Laplacian principal part
Authors: Bixiang Wang (New Mexico Inst. of Mining and Technology, Socorro, NM, USA)
Boling Guo (Inst. of Applied Physics and Comp. Math., Beijing, China)
Abstract:
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.