Non-autonomous attractors for integro-differential evolution equations

By Tomás Caraballo, Peter E. Kloeden. 2009

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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.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1a0bc87aafbb19d8aac50f57623eb7c668d79bb3