Global attracting sets and exponential stability of stochastic partial functional differential equations

Abstract

This paper is concerned with the global attracting sets and the exponential stability in the mean square of mild solutions for stochastic functional partial differential equations. Some new sufficient conditions ensuring the existence of the global attracting sets and the exponential stability in the mean square of mild solutions for the considered equations are established by introducing approximating systems with strong solutions and using a limiting argument. Finally, some examples are investigated to illustrate the theory.