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Pullback Attractors of Nonautonomous and Stochastic Multivalued Dynamical Systems

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Abstract

In this paper we study the existence of pullback global attractors for multivalued processes generated by differential inclusions. First, we define multivalued dynamical processes, prove abstract results on the existence of ω-limit sets and global attractors, and study their topological properties (compactness, connectedness). Further, we apply the abstract results to nonautonomous differential inclusions of the reaction–diffusion type in which the forcing term can grow polynomially in time, and to stochastic differential inclusions as well.

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Authors and Affiliations

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

    T. Caraballo & J. A. Langa

  2. Institute of Applied System Analysis, Pr. Pobedy 37, 252056-, Kiev, Ukraine

    V. S. Melnik

  3. Universidad Cardenal Herrera CEU, Comissari 3, 03203 Elche, Alicante, Spain

    J. Valero

Authors
  1. T. Caraballo
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  2. J. A. Langa
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  3. V. S. Melnik
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  4. J. Valero
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Caraballo, T., Langa, J.A., Melnik, V.S. et al. Pullback Attractors of Nonautonomous and Stochastic Multivalued Dynamical Systems. Set-Valued Analysis 11, 153–201 (2003). https://doi.org/10.1023/A:1022902802385

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  • DOI: https://doi.org/10.1023/A:1022902802385

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