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dc.contributor.authorBenoit, Eric ( )
dc.contributor.authorEl Hamidi, Abdallah ( )
dc.contributor.authorFruchard, Augustin ( )
dc.date.accessioned2020-08-10T21:02:56Z
dc.date.available2020-08-10T21:02:56Z
dc.date.issued2002-06-03
dc.identifier.citationBenoit, E., El Hamidi, A., & Fruchard, A. (2002). On combined asymptotic expansions in singular perturbations. Electronic Journal of Differential Equations, 2002(51), pp. 1-27.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12350
dc.description.abstractA structured and synthetic presentation of Vasil'eva's combined expansions is proposed. These expansions take into account the limit layer and the slow motion of solutions of a singularly perturbed differential equation. An asymptotic formula is established which gives the distance between two exponentially close solutions. An ``input-output" relation around a {\it canard} solution is carried out in the case of turning points. We also study the distance between two canard values of differential equations with given parameter. We apply our study to the Liouville equation and to the splitting of energy levels in the one-dimensional steady Schr\"{o}dinger equation in the double well symmetric case. The structured nature of our approach allows us to give effective symbolic algorithms.en_US
dc.formatText
dc.format.extent27 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSingular perturbationen_US
dc.subjectCombined asymptotic expansionen_US
dc.subjectTurning pointen_US
dc.subjectCanard solutionen_US
dc.titleOn Combined Asymptotic Expansions in Singular Perturbationsen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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