dc.contributor.author Benoit, Eric ( ) dc.contributor.author El Hamidi, Abdallah ( ) dc.contributor.author Fruchard, Augustin ( ) dc.date.accessioned 2020-08-10T21:02:56Z dc.date.available 2020-08-10T21:02:56Z dc.date.issued 2002-06-03 dc.identifier.citation Benoit, 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.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/12350 dc.description.abstract A 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.format Text dc.format.extent 27 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. dc.subject Singular perturbation en_US dc.subject Combined asymptotic expansion en_US dc.subject Turning point en_US dc.subject Canard solution en_US dc.title On Combined Asymptotic Expansions in Singular Perturbations en_US txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License.
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