Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems

Abstract

The existence of uniform attractor in l2×l2 is proved for the partly dissipative nonautonomous lattice systems with a new class of external terms belonging to Lloc2(R,l2), which are locally asymptotic smallness and translation bounded but not translation compact in Lloc2(R,l2). It is also showed that the family of processes corresponding to nonautonomous lattice systems with external terms belonging to weak topological space possesses uniform attractor, which is identified with the original one. The upper semicontinuity of uniform attractor is also studied.