Global and exponential attractors for nonlinear reaction–diffusion systems in unbounded domains

Abstract

We study the long-time behaviour of solutions of autonomous and non-autonomous reaction-diffusion equations in unbounded domains of R3. It is shown that, under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess compact global (uniform) attractors in the corresponding phase space. Estimates for Kolmogorov's ε-entropy of these attractors in terms of Kolmogorov's entropy of the external forces are given. Moreover, (infinite-dimensional) exponential attractors with the same entropy estimate as that of the corresponding global (uniform) attractor are also constructed.