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Differential and Difference Equations with Applications pp 217–225Cite as

Pullback Attractors for NonAutonomous Dynamical Systems

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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References

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Authors and Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, c/Tarfia s/n, 41012, Sevilla, Spain

    María Anguiano, Tomás Caraballo & José Real

  2. Dpto. Estadística y Matemática Aplicada, Universidad Miguel Hernández, Avda. de la Universidad s/n, 03202, Elche, Spain

    José Valero

Authors
  1. María Anguiano
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  2. Tomás Caraballo
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  3. José Real
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  4. José Valero
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Corresponding author

Correspondence to María Anguiano .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Anguiano, M., Caraballo, T., Real, J., Valero, J. (2013). Pullback Attractors for NonAutonomous Dynamical Systems. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_15

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