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 Model. Anal. Inform. Sist., 2017, Volume 24, Number 3, Pages 280–287 (Mi mais564)

Singularly perturbed elliptic Dirichlet problem with three-band boundary layer

V. A. Beloshapko

Lomonosov Moscow State University, 1 Leninskiye Gory, Moscow 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 three-zone boundary layer arises in the vicinity of the domain boundary with a different scale of boundary-layer variables and a different behaviour of the solution in different zones. The asymptotic expansion of the solution being in fractional powers of the small parameter, boundary-layer series are constructed using a non-standard algorithm. A complete asymptotic expansion of the solution is constructed and justified.

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, project No 15-01-04619.

DOI: https://doi.org/10.18255/1818-1015-2017-3-280-287

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UDC: 519.632.34

Citation: V. A. Beloshapko, “Singularly perturbed elliptic Dirichlet problem with three-band boundary layer”, Model. Anal. Inform. Sist., 24:3 (2017), 280–287

Citation in format AMSBIB
\Bibitem{Bel17} \by V.~A.~Beloshapko \paper Singularly perturbed elliptic Dirichlet problem with three-band boundary layer \jour Model. Anal. Inform. Sist. \yr 2017 \vol 24 \issue 3 \pages 280--287 \mathnet{http://mi.mathnet.ru/mais564} \crossref{https://doi.org/10.18255/1818-1015-2017-3-280-287} \elib{http://elibrary.ru/item.asp?id=29332971}