Pullback attractors for multi-valued non-compact random dynamical systems generated by reaction-diffusion equations on an unbounded domain

摘要

In this paper we study pullback attractors of reaction-diffusion equations on an unbounded domain with non-autonomous deterministic as well as stochastic forcing terms for which the uniqueness of solutions need not hold. We first present the existence and structure of pullback attractors of multi-valued non-compact random dynamical systems. Then we prove the existence of pullback attractors in L-2(R-n), L-p(R-n) and H-1(R-n) for multi-valued non-compact random dynamical systems associated with the reaction-diffusion equations on R-n, and the identical relation of pullback attractors in different spaces is also provided. In particular, the measurability of pullback attractors is established for reaction-diffusion equations on R-n. (C) 2015 Elsevier Inc. All rights reserved.