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Regularity and structure of pullback attractors for reaction-diffusion type systems without uniqueness

 

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Opened Access Regularity and structure of pullback attractors for reaction-diffusion type systems without uniqueness
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Author: Cui, Hongyong
Langa Rosado, José Antonio
Li, Yangrong
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016-07
Published in: Nonlinear Analysis: Theory, Methods and Applications, 140, 208-235.
Document type: Article
Abstract: In this paper, we study the pullback attractor for a general reaction-diffusion system for which the uniqueness of solutions is not assumed. We first establish some general results for a multi-valued dynamical system to have a bi-spatial pullback attractor, and then we find that the attractor can be backwards compact and composed of all the backwards bounded complete trajectories. As an application, a general reaction-diffusion system is proved to have an invariant (H, V )-pullback attractor A = {A(τ)}τ∈R. This attractor is composed of all the backwards compact complete trajectories of the system, pullback attracts bounded subsets of H in the topology of V, and moreover ∪ s6τ A(s) is precompact in V, ∀τ ∈ R. A non-autonomous Fitz-Hugh-Nagumo equation is studied as a specific example of the reaction–diffusion system.
Cite: Cui, H., Langa Rosado, J.A. y Li, Y. (2016). Regularity and structure of pullback attractors for reaction-diffusion type systems without uniqueness. Nonlinear Analysis: Theory, Methods and Applications, 140, 208-235.
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URI: http://hdl.handle.net/11441/49529

DOI: 10.1016/j.na.2016.03.012

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