Averaging of multivalued differential equations
type: Item
instance of: scholarly article
title: Averaging of multivalued differential equations
zbMATH Open document ID: 1036.34013
DOI: 10.1155/S016117120300680X
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/50731
review text: Here, the following nonlinear perturbed differential inclusion is investigated \[ z'(t)\in\varepsilon F(z(t),y(t)),\quad y'(t)\in G(y(t)), \] where \(\varepsilon >0\) is the perturbation parameter, \(t\in [0,T/\varepsilon]\), \(z\) is the slow motion and \(y\) the fast motion. Additionally, \(F\) and \(G\) are assumed to be Lipschitz continuous in Hausdorff sense, with compact, convex and nonempty values. The author shows that, under a transitivity condition on the fast subsystem, there exists an averaged system whose trajectories approximate, uniformly in Hausdorff sense, the slow trajectories of the original one. Moreover, the approximation is of order \(O(\varepsilon^{\frac{1}{3}})\), as \(\varepsilon\rightarrow 0\).
reviewed by: Nikos Yannakakis
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 1930050
zbMATH Keywords: Differential inclusions
zbMATH Keywords: slow and fast subsystem
zbMATH Keywords: averaging method
zbMATH Keywords: perturbed system
zbMATH Keywords: invariant measure
zbMATH Keywords: approximation order
zbMATH Keywords: multifunction
zbMATH Keywords: solution map
zbMATH Keywords: measurable selection
author: Götz Grammel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1930050