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

Pages: 1073 - 1100, Volume 26, Issue 3, March 2010

doi:10.3934/dcds.2010.26.1073       Abstract        Full Text (355.2K)       Related Articles

Antônio Luiz Pereira - Instituto de Matemática e Estatística-Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, CEP 05508-090, São Paulo-SP, Brazil (email)
Severino Horácio da Silva - 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, Brazil (email)

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.

Received: February 2009;      Revised: September 2009;      Published: December 2009.