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Duck trajectories in multidimensional singularly perturbed systems with a single fast variable

Duck trajectories in multidimensional singularly perturbed systems with a single fast variable Differential Equations, Vol. 40, No. 10, 2004, pp. 1373–1382. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 10, 2004, pp. 1305–1313. Original Russian Text Copyright c 2004 by Bobkova. ORDINARY DIFFERENTIAL EQUATIONS Duck Trajectories in Multidimensional Singularly Perturbed Systems with a Single Fast Variable A. S. Bobkova Moscow State University, Moscow, Russia Received June 23, 2003 In the study of singularly perturbed systems of ordinary di erential equations, one faces at rst sight rather unexpected phenomenon of duck trajectories. As a rule, they arise owing to the failure of certain assumptions under which, as was shown in [1, p. 57], a singularly perturbed system with a small parameter muptiplying part of the derivatives can be represented as a C perturbation of the corresponding degenerate system. First duck trajectories were detected in 1978 by the French mathematicians F. Diener and M. Diener with the use of nonstandard analysis. Later duck trajectories were considered by other authors with the use of nonstandard analysis as well as in the framework of standard asymptotic analysis. The case of a singularly perturbed system with two slow variables (and one fast variable) was considered in [2], where sucient conditions for the appearance of duck trajectories were http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Duck trajectories in multidimensional singularly perturbed systems with a single fast variable

Bobkova, A.
Differential Equations , Volume 40 (10) – Feb 23, 2005
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/s10625-005-0058-9
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 40, No. 10, 2004, pp. 1373–1382. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 10, 2004, pp. 1305–1313. Original Russian Text Copyright c 2004 by Bobkova. ORDINARY DIFFERENTIAL EQUATIONS Duck Trajectories in Multidimensional Singularly Perturbed Systems with a Single Fast Variable A. S. Bobkova Moscow State University, Moscow, Russia Received June 23, 2003 In the study of singularly perturbed systems of ordinary di erential equations, one faces at rst sight rather unexpected phenomenon of duck trajectories. As a rule, they arise owing to the failure of certain assumptions under which, as was shown in [1, p. 57], a singularly perturbed system with a small parameter muptiplying part of the derivatives can be represented as a C perturbation of the corresponding degenerate system. First duck trajectories were detected in 1978 by the French mathematicians F. Diener and M. Diener with the use of nonstandard analysis. Later duck trajectories were considered by other authors with the use of nonstandard analysis as well as in the framework of standard asymptotic analysis. The case of a singularly perturbed system with two slow variables (and one fast variable) was considered in [2], where sucient conditions for the appearance of duck trajectories were

Journal

Differential Equations – Springer Journals

Published: Feb 23, 2005

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