Partly dissipative systems in uniformly local spaces
Volume 100 / 2004
Colloquium Mathematicum 100 (2004), 221-242
MSC: 35B41, 35B40, 35K45, 35K57.
DOI: 10.4064/cm100-2-6
Abstract
We study the existence of attractors for partly dissipative systems in ${\mathbb R}^n$. 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 ${\mathbb R}^n$ and to Field–Noyes equations in ${\mathbb R}$. Some embeddings between uniformly local spaces are also proved.
