Compact uniform attractors for dissipative lattice dynamical systems with delays

Abstract

In this paper, weconsider the long time behavior of solutions for dissipative latticedynamical systems with delays. We first prove a sufficient andnecessary condition for the existence of a compact uniform attractorfor the family of processes corresponding to the lattice dynamicalsystems with delays. Then we apply this result to prove theexistence of a compact uniform attractor for the process associatedto the retarded lattice Zakharov equations. As a consequence, someresults for the non-delay lattice dynamical systems are deduced asparticular cases.