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Article Contents

# Compact uniform attractors for dissipative lattice dynamical systems with delays

• In this paper, we consider the long time behavior of solutions for dissipative lattice dynamical systems with delays. We first prove a sufficient and necessary condition for the existence of a compact uniform attractor for the family of processes corresponding to the lattice dynamical systems with delays. Then we apply this result to prove the existence of a compact uniform attractor for the process associated to the retarded lattice Zakharov equations. As a consequence, some results for the non-delay lattice dynamical systems are deduced as particular cases.
Mathematics Subject Classification: 35B40; 37L50; 35Q55.

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