Attractors for partly dissipative lattice dynamic systems in

In this paper, we study the asymptotic behavior of solutions for the partly dissipative lattice dynamical systems in l 2 × l 2 . We prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in l 2 × l 2 . The upper semicontinuity of the global attractor is also considered by finite-dimensional approximations of attractors for the lattice systems.