Partly dissipative systems in uniformly local spaces

Volume 100 / 2004

Alexandre N. Carvalho, Tomasz Dlotko Colloquium Mathematicum 100 (2004), 221-242 MSC: 35B41, 35B40, 35K45, 35K57. DOI: 10.4064/cm100-2-6


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.


  • Alexandre N. CarvalhoDepartamento 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
  • Tomasz DlotkoInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland

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