Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation

In this paper we study the long-time behaviour of solutions of reaction-diffusion equations (RDEs) in unbounded domains of R-n. In particular, we prove that, under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess infinite-dimensional exponential attractors whose Kolmogorov epsilon-entropy satisfies an estimate of the same type as that obtained previously for the epsilon-entropy of the global attractor. Moreover, we also study the problem of the approximation of these infinite-dimensional exponential attractors by finite-dimensional ones associated with the same RDEs in bounded domains.