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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 77–80 (Mi into170)  

This article is cited in 4 scientific papers (total in 4 papers)

Singularly perturbed system of parabolic equations in the critical case

A. S. Omuralieva, S. Kulmanbetovab

a Kyrgyzstan-Turkey "MANAS" University, Bishkek
b Naryn State University, Naryn, Kyrgyzstan
Full-text PDF (136 kB) Citations (4)
Abstract: We examine a system of singularly perturbed parabolic equations in the case where the small parameter is involved as a coefficient of both time and spatial derivatives and the spectrum of the limit operator has a multiple zero point. In such problems, corner boundary layers appear, which can be described by products of exponential and parabolic boundary-layer functions. Under the assumption that the limit operator is a simple-structure operator, we construct a regularized asymptotics of a solution, which, in addition to corner boundary-layer functions, contains exponential and parabolic boudary-layer functions. The construction of the asymptotics is based on the regularization method for singularly perturbed problems developed by S. A. Lomov and adapted to singularly perturbed parabolic equations with two viscous boundaries by A. S. Omuraliev.
Keywords: singularly perturbed parabolic equation, parabolic boundary layer, regularized asymptotics, exponential boundary layer.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 728–731
DOI: https://doi.org/10.1007/s10958-018-3778-0
Bibliographic databases:
Document Type: Article
UDC: 517.956.4
MSC: 35K51,35B25
Language: Russian
Citation: A. S. Omuraliev, S. Kulmanbetova, “Singularly perturbed system of parabolic equations in the critical case”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 77–80; J. Math. Sci. (N. Y.), 230:5 (2018), 728–731
Citation in format AMSBIB
\Bibitem{OmuKul17}
\by A.~S.~Omuraliev, S.~Kulmanbetova
\paper Singularly perturbed system of parabolic equations in the critical case
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 77--80
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into170}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801390}
\zmath{https://zbmath.org/?q=an:1391.35190}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 728--731
\crossref{https://doi.org/10.1007/s10958-018-3778-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044469669}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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