ATTRACTORS FOR NONAUTONOMOUS EVOLUTION-EQUATIONS WITH ALMOST PERIODIC SYMBOLS

We present a new approach for studying attractors for nonautonomous evolution equations. We introduce the notion of the time symbol sigma(t) for nonautonomus evolution equations. We study here the case when the symbol sigma(t) is almost periodic in t with values in a suitable Banach space. To every such evolution equation corresponds a family of processes. We establish the existence and the structure of the uniform attractor of this family and we construct the attractor for the initial evolution equation. We construct the attractors for the nonautonomous 2D Navier-Stokes equations, nonautonomous reaction-diffusion system, nonautonomous dissipative hyperbolic equations and for other equations.