Asymptotic behavior of non-autonomous lattice systems

The asymptotic behavior of non-autonomous infinite-dimensional lattice systems is studied. It is shown that the non-autonomous lattice reaction–diffusion system has a compact uniform attractor. The uniform asymptotic compactness of the system is established by showing that the tails of the solutions are uniformly small when time goes to infinity. The upper semicontinuity of uniform attractors is also obtained when the infinite-dimensional reaction–diffusion system is approached by a family of finite-dimensional systems.