Continuity of  global attractors   for a class  of non local evolution equations

Antônio Luiz Pereira; Severino Horácio da Silva

doi:10.3934/dcds.2010.26.1073

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2010, Volume 26, Issue 3: 1073-1100. Doi: 10.3934/dcds.2010.26.1073

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Continuity of global attractors for a class of non local evolution equations

Antônio Luiz Pereira^1, and
Severino Horácio da Silva^2,

1.
Instituto de Matemática e Estatística-Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, CEP 05508-090, São Paulo-SP
2.
Unidade Acadêmica de Matemática e Estatística UAME/CCT/UFCG, Avenida Aprígio Veloso, 882, Bairro Universitrio, Caixa Postal: 10.044, CEP 58109-970, Campina Grande-PB

Received: January 31, 2009

Revised: August 31, 2009

Published: August 2010

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Abstract

In this work we prove that the global attractors for the flow of the equation

$\frac{\partial m(r,t)}{\partial t}=-m(r,t)+ g(\beta J $∗$ m(r,t)+ \beta h),\ h ,\ \beta \geq 0,$

are continuous with respect to the parameters $h$ and $\beta$ if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

Keywords:

Global attractor; Normal hyperbolicity; Continuity of attractors.

Mathematics Subject Classification: Primary: 34G20; Secondary: 47H15.

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