On Combined Asymptotic Expansions in Singular Perturbations

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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.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 <i>canard</i> 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 Schrödinger equation in the double well symmetric case. The structured nature of our approach allows us to give effective symbolic algorithms.
dc.description.departmentMathematics
dc.formatText
dc.format.extent27 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBenoit, E., El Hamidi, A., & Fruchard, A. (2002). On combined asymptotic expansions in singular perturbations. <i>Electronic Journal of Differential Equations, 2002</i>(51), pp. 1-27.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/12350
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSingular perturbation
dc.subjectCombined asymptotic expansion
dc.subjectTurning point
dc.subjectCanard solution
dc.titleOn Combined Asymptotic Expansions in Singular Perturbations
dc.typeArticle

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