Pullback Attractors for NonAutonomous Dynamical Systems
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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.
KeywordsPullback attractor Non-autonomous reaction-diffusion equation Set-valued dynamical system Unbounded domain
- 1.Anguiano, M.: Atractores para EDP parabólicas no lineales y no autónomas en dominios no acotados. Ph.D. Dissertation, Universidad de Sevilla (2011)Google Scholar
- 4.Anguiano, M., Caraballo, T., Real, J., Valero, J.: Pullback attractors for reaction-diffusion equations in some unbounded domains with an H −1-valued non-autonomous forcing term and without uniqueness of solutions. Discret. Contin. Dyn. Syst. Ser. B 14(2), 307–326 (2010)MathSciNetCrossRefzbMATHGoogle Scholar