On the existence of the compact global attractor for semilinear reaction diffusion systems on ℝ^N

We show that a class of reaction diffusion systems on R^N generates an asymptotically compact semiflow on the Banach space of bounded uniformly continuous functions. If such a semiflow is dissipative, then a unique, non-empty, compact minimal attractor is known to exist. We apply this abstract result to obtain the existence of the compact minimal attractor for reaction diffusion systems on R^N that contain appropriate weight functions. We also state conditions, which guarantee that the attractor has finite Hausdorff-dimension. © 1996 Academic Press, Inc.