Global Attractors of Non-autonomous Lattice Dynamical Systems

Abstract

The aim of this paper is studying the compact global attractors for non-autonomous lattice dynamical systems of the form $u_i^{\prime }=\hat{I}½(u_{i-1}-2u_i+u_{i+1})-\hat{I}»u_i+f(u_i)+f_i(t)(i\in \mathbb{Z},\hat{I}»>0)$. We prove their dissipativness, asymptotic compactness and then the existence of compact global attractors.