Artículo
Regularity and structure of pullback attractors for reaction-diffusion type systems without uniqueness
Autor/es | Cui, Hongyong
Langa Rosado, José Antonio Li, Yangrong |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2016-07 |
Fecha de depósito | 2016-12-01 |
Publicado en |
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Resumen | 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 ... 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. |
Identificador del proyecto | FQM-1492
info:eu-repo/grantAgreement/EC/FP7/318999 11571283 |
Cita | 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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