We study the existence of the uniform global attractor for a family of Klein-Gordon-Schrödinger non-autonomous infinite dimensional lattice dynamical systems with nonlinear part of the form f (u, v, t), where we introduce a suitable Banach space of functions W and we assume that f (·,·, t) is an element of the hull of an almost periodic function f0 (·,·, t) with values in W.
1. Introduction. Lattice dynamical systems (LDSs) are infinite systems of ordinary differential equations or of difference equations, indexed by points in a lattice such as the unbounded n-dimensional integer lattice Zn. They appear in a wide variety of applications and in many fields, such as chemical reaction theory [22, 25], electrical engineering [33], propagation of nerve pulses in myelinated axons [7, 8, 26, 27], pattern recognition [16, 17, 18], image processing [19, 20, 21], etc. The global attractor is a significant tool to study the long time behavior of a given dynamical system since it is the smallest compact set, with respect to inclusion, that is invariant and attracts all the trajectories originated from the whole phase space. From [34], we know that it is difficult to estimate the attractor of the solution semiflow generated by the initial value problem of dissipative partial differential equations (PDEs) on unbounded domains because, in general, it is infinite-dimensional. Therefore it is significant to study the LDSs corresponding to the initial value problem of PDEs on unbounded domains because of the importance of such systems and they can be regarded as an approximation to the corresponding continuous PDEs. The existence of global attractors, uniform attractors, pullback attractors, and …