ATTRACTORS FOR FIRST ORDER LATTICE SYSTEMS WITH ALMOST PERIODIC NONLINEAR PART

We study the existence of the uniform global attractor for a family of infinite dimensional first order non-autonomous lattice dynamical systems of the following form: (u) over dot + Au + alpha u f (u, t) = g (t) , (g, f) is an element of H ((g(0), f(0))), t > tau, tau is an element of R, with initial data u (tau) = u(tau). The nonlinear part of the system f (u, t) presents the main difficultly of this work. To overcome this difficulty we introduce a suitable Banach space W of functions satisfying (3)-(7) with norm (8) such that f(0) (., t) is an almost periodic function of t with values in W and (g, f) is an element of H ((g(0), f(0))).