Upper Semicontinuity of Random Attractors for Non-compact Random Dynamical Systems

TL;DR

This paper proves the upper semicontinuity of random attractors in non-compact random dynamical systems and applies the result to stochastic reaction-diffusion equations with white noise on unbounded domains.

Contribution

It establishes the upper semicontinuity of random attractors under certain conditions and applies this to stochastic reaction-diffusion systems on R^n.

Findings

Proved upper semicontinuity of random attractors for non-compact systems.

Applied the theoretical result to stochastic reaction-diffusion equations.

Demonstrated precompactness of the union of perturbed attractors with probability one.

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.