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Pullback Attractors for NonAutonomous Dynamical Systems

  • María AnguianoEmail author
  • Tomás Caraballo
  • José Real
  • José Valero
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 47)

Abstract

We study a nonautonomous reaction-diffusion equation with zero Dirichlet boundary condition, in an unbounded domain containing a nonautonomous forcing term taking values in the space H −1, and with a continuous nonlinearity which does not ensure uniqueness of solution. Using results of the theory of set-valued nonautonomous (pullback) dynamical systems, we prove the existence of minimal pullback attractors for this problem. We ensure that the pullback attractors are connected and also establish the relation between these attractors.

Keywords

Pullback attractor Non-autonomous reaction-diffusion equation Set-valued dynamical system Unbounded domain 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • María Anguiano
    • 1
    Email author
  • Tomás Caraballo
    • 1
  • José Real
    • 1
  • José Valero
    • 2
  1. 1.Dpto. Ecuaciones Diferenciales y Análisis NuméricoUniversidad de SevillaSevillaSpain
  2. 2.Dpto. Estadística y Matemática AplicadaUniversidad Miguel HernándezElcheSpain

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