UPPER SEMICONTINUITY OF UNIFORM RANDOM ATTRACTORS FOR DELAY PARABOLIC EQUATION

Abstract

This paper concentrates on the upper semicontinuity of uniform random attractors for a class of delay parabolic equations with additive noise and nonautonomous external force terms. Firstly, through the uniform estimation of the solution, it is proved that the solution of the equation has a closed uniform pullback absorbing set with respect to the symbolic space. Then, by Arzela-Ascoli theorem, we prove uniformly pullback compactness of solutions as well as the existence and uniqueness of uniform random attractors. Finally, we prove the upper semicontinuity of the uniform random attractors when time delay approaches to zero.