This article is cited in 2 papers

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.

UDC: 519.632.34

Received: 15.12.2016

DOI: 10.18255/1818-1015-2017-3-280-287

Bibliographic databases:

•