Partly dissipative systems in uniformly local spaces

Abstract

We study the existence of attractors for partly dissipative systems in ℝn. For these systems we prove the existence of global attractors with attraction properties and compactness in a slightly weaker topology than the topology of the phase space. We obtain abstract results extending the usual theory to encompass such two-topologies attractors. These results are applied to the FitzHugh-Nagumo equations in ℝn and to Field-Noyes equations in ℝ. Some embeddings between uniformly local spaces are also proved.