Approximation of Attractors of Nonautonomous Lattice Dynamical Systems

Abstract

The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_{i}'=ν(u_{i-1}-2u_i+u_{i+1})-λu_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z)\ (*)$. We show that the finite-dimensional approximations for (*) are uniformly dissipative. The upper semi-continuous convergence of the attractors of the finite-dimensional approximations is established.