Article
Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system
Author/s | Carvalho, Alexandre Nolasco
Langa Rosado, José Antonio Robinson, James C. Suárez Fernández, Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2007-05-15 |
Deposit Date | 2016-07-06 |
Published in |
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Abstract | 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 ... 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. |
Citation | 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. |
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