Set-Valued Analysis

, Volume 11, Issue 2, pp 153–201

Pullback Attractors of Nonautonomous and Stochastic Multivalued Dynamical Systems

  • T. Caraballo
  • J. A. Langa
  • V. S. Melnik
  • J. Valero
Article

DOI: 10.1023/A:1022902802385

Cite this article as:
Caraballo, T., Langa, J.A., Melnik, V.S. et al. Set-Valued Analysis (2003) 11: 153. doi:10.1023/A:1022902802385

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.

attractorasymptotic behaviourdifferential inclusionreaction–diffusion equationnonautonomous dynamical system

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • T. Caraballo
    • 1
  • J. A. Langa
    • 1
  • V. S. Melnik
    • 2
  • J. Valero
    • 3
  1. 1.Departamento de Ecuaciones Diferenciales y Análisis NuméricoUniversidad de SevillaSevillaSpain
  2. 2.Institute of Applied System AnalysisKievUkraine
  3. 3.Universidad Cardenal Herrera CEU, Comissari 3AlicanteSpain