Asymptotic behavior of stochastic nonlocal partial differential equations on unbounded domains

This paper is concerned with the asymptotic behavior of solutions for a class of stochastic nonlocal partial differential equations driven by additive white noise on unbounded domains. We first prove the existence of a continuous non-autonomous random dynamical system for the equations. Next, we establish the uniform estimates of solutions by carefully estimating the nonlocal term. Finally, we show the existence and uniqueness of random attractors. We utilize the methods of spectral decomposition and the uniform tail-estimates to overcome the difficulties caused by the lack of compact Sobolev embedding on unbounded domains and the weak dissipative structure of the equations.