Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 139, pp. 1-18.

Title: Upper semicontinuity of random attractors for  
       non-compact random dynamical systems

Author: Bixiang Wang (New Mexico Inst. of Mining and Tech., NM, USA)

Abstract:
 The upper semicontinuity of random attractors
 for non-compact random dynamical systems is proved
 when the union of all perturbed random attractors
 is precompact with probability one. This result is applied
 to the stochastic Reaction-Diffusion  with white noise
 defined on the entire space R^n.

Submitted June 18, 2009. Published October 30, 2009.
Math Subject Classifications: 37L55, 60H15, 35B40.
Key Words: Stochastic Reaction-Diffusion equation; random attractor; 
           asymptotic compactness; upper semicontinuity.