KOLMOGOROV EPSILON-ENTROPY ESTIMATES FOR THE UNIFORM ATTRACTORS OF NONAUTONOMOUS REACTION-DIFFUSION SYSTEMS

The Kolmogorov E-entropy of the uniform attractor A of a family of non autonomous reaction-diffusion systems with external forces g(x,t) is s tudied. The external forces g(x, t) are assumed to belong to some subs et Sigma of C(R; H), where H = (L-2(Omega))(N), that is invariant unde r the group of t-translations. Furthermore, Sigma is compact in C(R; H ). An estimate for the epsilon-entropy of the uniform attractor A is g iven in terms of the epsilon(1) = epsilon(1)(epsilon)-entropy of the c ompact subset Sigma(0,1) of C([0, l]; H) consisting of the restriction s of the external forces g(x,t) is an element of Sigma to the interval [0, l], l = l(epsilon) (here epsilon(1)(epsilon) similar to mu epsilo n and l(epsilon) similar to tau log(2)(1/epsilon)). This general estim ate is illustrated by several examples from different fields of mathem atical physics and information theory.