Partly dissipative systems in uniformly local spaces

Alexandre N. Carvalho¹ ; Tomasz Dlotko²

¹ Departamento de Matemática Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo-Campus de São Carlos Caixa Postal 668 13560-970 São Carlos SP, Brazil
² Institute of Mathematics Silesian University 40-007 Katowice, Poland

Colloquium Mathematicum, Tome 100 (2004) no. 2, pp. 221-242.

Résumé

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.

Détail

DOI : 10.4064/cm100-2-6

Mots-clés : study existence attractors partly dissipative systems mathbb these systems prove existence global attractors attraction properties compactness slightly weaker topology topology phase space obtain abstract results extending usual theory encompass two topologies attractors these results applied fitzhugh nagumo equations mathbb field noyes equations mathbb embeddings between uniformly local spaces proved