Global Attractors and Steady State Solutions for a Class of Reaction–Diffusion Systems

We show that weakLpdissipativity implies strongL∞dissipativity and therefore implies the existence of global attractors for a general class of reaction–diffusion systems. This generalizes the results of Alikakos and Rothe. The results on positive steady states (especially for systems of three equations) in our earlier work (J. Differential Equations130(1996), 59–91) are improved.