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Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system

Opened Access Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system

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Autor: Carvalho, Alexandre Nolasco
Langa Rosado, José Antonio
Robinson, James C.
Suárez Fernández, Antonio
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2007-05-15
Publicado en: Journal of Differential Equations, 236 (2), 570-603.
Tipo de documento: Artículo
Resumen: In this paper we determine the exact structure of the pullback attractors in non-autonomous problems that are perturbations of autonomous gradient systems with attractors that are the union of the unstable manifolds of a finite set of hyperbolic equilibria. We show that the pullback attractors of the perturbed systems inherit this structure, and are given as the union of the unstable manifolds of a set of hyperbolic global solutions which are the non-autonomous analogues of the hyperbolic equilibria. We also prove, again parallel to the autonomous case, that all solutions converge as t → +∞ to one of these hyperbolic global solutions. We then show how to apply these results to systems that are asymptotically autonomous as t → −∞ and as t → +∞, and use these relatively simple test cases to illustrate a discussion of possible definitions of a forwards attractor in the non-autonomous case.
Cita: Carvalho, A.N., Langa Rosado, J.A., Robinson, J.C. y Suárez Fernández, A. (2007). Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Journal of Differential Equations, 236 (2), 570-603.
Tamaño: 387.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43236

DOI: 10.1016/j.jde.2007.01.017

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