Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time

Abstract

Producción CientíficaNew results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate boundedness of the solutions of the layer problems, inflated pullback attractors are considered. In general, one cannot disregard the inflated version of the pullback attractor, but it is possible under the continuity of the fiber projection map of the attractor. The problem of the limit of the solutions of the slow-fast system at each fixed positive value of the slow time is also treated and in this formulation the critical set is given by the union of the fibers of the pullback attractors. The results can be seen as extensions of the classical Tikhonov theorem to the nonautonomous setting.Este trabajo forma parte de los proyectos de investigación: MICIIN/FEDER Grant PID2021-125446NB-I00, Universidad de Valladolid Grant PIP-TCESC-2020, y UKRI Grant EP/X027651/1

Similar works

Full text

thumbnail-image

Repositorio Documental de la Universidad de Valladolid

redirect
Last time updated on 28/10/2024

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.

Licence: info:eu-repo/semantics/openAccess