Finite-Dimensional Attractors Associated with Partly Dissipative Reaction-Diffusion Systems

Abstract

The long-time behavior of the solutions of some partly dissipative reaction-diffusion systems is studied. Two types of problems are considered: systems with a polynomial growth nonlinearity, and systems admitting a positively invariant region. It is shown that the long-time behavior can be described by a universal attractor, and bounds of the Hausdorff and fractal dimensions of this attractor are derived. The results are applied to several classical systems borrowed from mathematical biology, physics and chemistry.