Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains

SeMA Journal volume 51, pages9–16(2010)Cite this article

Abstract

The existence of a pullback attractor in L2 (Ω) for the following non-autonomous reaction-diffusion equation #### (1) is proved in this paper, when the domain Ω is not necessarily bounded but satisfying the Poincaré inequality, and h ∈ L 2loc (ℝ; H−1 (Ω)). The main concept used in the proof is the asymptotic compactness of the process generated by the problem.

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Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain

    María Anguiano

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  1. María Anguiano
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Correspondence to María Anguiano.

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Anguiano, M. Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains. SeMA 51, 9–16 (2010). https://doi.org/10.1007/BF03322548

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Key words

  • pullback attractor
  • asymptotic compactness
  • evolution process
  • non-autonomous reaction-diffusion equation

AMS subject classifications

  • 35B41
  • 35Q35
  • 35Q30
  • 35K90
  • 37L30