Continuity of attractors

  • Alexandre N. Carvalho
  • José A. Langa
  • James C. Robinson
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 182)

Abstract

In this chapter we study the continuity of attractors under perturbation. The problems of upper semicontinuity (‘no explosion’) and lower semicontinuity (‘no implosion’) are distinct, and we will treat them separately. Broadly speaking, one expects upper semicontinuity to hold widely, but lower semicontinuity requires structural assumptions on the unperturbed process and its attractor.

Keywords

Manifold Carbone 

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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Alexandre N. Carvalho
    • 1
  • José A. Langa
    • 2
  • James C. Robinson
    • 3
  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil
  2. 2.Departamento de Ecuaciones Diferenciales y Análisis NuméricoFacultad de MatemáticasSevilleSpain
  3. 3.Mathematics InstituteUniversity of WarwickCoventryUK

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