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dc.contributor.authorLobry, Claude
dc.contributor.authorSari, Tewfik
dc.contributor.authorTouhami, Sefiane
dc.date.accessioned2019-03-25T19:46:15Z
dc.date.available2019-03-25T19:46:15Z
dc.date.issued1998-07-09
dc.date.submitted1997-09-30
dc.identifier.citationLobry, C., Sari, T. & Touhami, S. (1998). On Tykhonov's theorem for convergence of solutions of slow and fast systems. "Electronic Journal of Differential Equations," Vol. 1998, No. 19, pp. 1-22.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/7939
dc.description.abstractSlow and fast systems gain their special structure from the presence of two time scales. Their analysis is achieved with the help of Singular Perturbation Theory. The fundamental tool is Tykhonov's theorem which describes the limiting behaviour, for compact interval of time, of solutions of the perturbed system which is a one-parameter deformations of the so-called unperturbed system. Our aim here is to extend this description to the solutions of all systems that belong to a small neighbourhood of the unperturbed system. We investigate also the behaviour of solutions on the infinite time interval. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is an axiomatic approach to Nonstandard Analysis.en_US
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 1998, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSingular perturbationsen_US
dc.subjectDeformationsen_US
dc.subjectAsymptotic stabilityen_US
dc.subjectNonstandard analysisen_US
dc.titleOn Tykhonov's Theorem for Convergence of Solutions of Slow and Fast Systemsen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons Attribution 4.0 International License https://creativecommons.org/licenses/by/4.0/


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