Article
Non-Autonomous Attractor for Integro-Differential Evolution Equations
Author/s | Caraballo Garrido, Tomás
Kloeden, Peter E. |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2009 |
Deposit Date | 2015-04-08 |
Published in |
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Abstract | We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an ... We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an infinite delay. Moreover, when conditions guaranteeing uniqueness of solutions do not hold, they generate a non-autonomous (possibly) multi-valued dynamical system (MNDS). The pullback attractors here are defined with respect to a universe of subsets of the state space with sub-exponetial growth, rather than restricted to bounded sets. The theory of non-autonomous pullback attractors is extended to such MNDS in a general setting and then applied to the original integro-differential equations. Examples based on the logistic equations with and without a diffusion term are considered. |
Citation | Caraballo Garrido, T. y Kloeden, P.E. (2009). Non-Autonomous Attractor for Integro-Differential Evolution Equations. Discrete and Continuous Dynamical Systems. Series S, 2 (1), 17-36. |
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