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 Model. Anal. Inform. Sist., 2016, Volume 23, Number 5, Pages 515–528 (Mi mais518)

Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation

V. F. Butuzov, V. A. Beloshapko

Lomonosov Moscow State University, GSP-1, 1-2 Leninskiye Gory, 119991, Russia

Abstract: A singularly perturbed elliptic problem with Dirichlet boundary conditions is considered in the case of multiple roots of the degenerate equation. A complete asymptotic expansion of the solution is constructed and justified. It is qualitatively different from the known expansion in the case where the root of the degenerate equation is simple: the asymptotic expansion of the solution being in fractional powers of the small parameter, boundary-layer variables have a different scale, boundary-layer series is constructed using a non-standard algorithm, the boundary layer in the vicinity of the domain boundary consists of three zones with different behavior of the solution in different zones.

Keywords: singularly perturbed elliptic equation, case of multiple root of the degenerate equation, asymptotic expansion of boundary layer type solution, three-band boundary layer.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-01-04619_à This work was supported by RFBR under the Grant No 15-01-04619.

DOI: https://doi.org/10.18255/1818-1015-2016-5-515-528

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UDC: 519.632.34

Citation: V. F. Butuzov, V. A. Beloshapko, “Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation”, Model. Anal. Inform. Sist., 23:5 (2016), 515–528

Citation in format AMSBIB
\Bibitem{ButBel16} \by V.~F.~Butuzov, V.~A.~Beloshapko \paper Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation \jour Model. Anal. Inform. Sist. \yr 2016 \vol 23 \issue 5 \pages 515--528 \mathnet{http://mi.mathnet.ru/mais518} \crossref{https://doi.org/10.18255/1818-1015-2016-5-515-528} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3569848} \elib{http://elibrary.ru/item.asp?id=27202301} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Beloshapko, “Cingulyarno vozmuschennaya ellipticheskaya zadacha Dirikhle s trekhzonnym pogranichnym sloem”, Model. i analiz inform. sistem, 24:3 (2017), 280–287
2. A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Comput. Math. Math. Phys., 58:12 (2018), 1977–1988
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