Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer
https://doi.org/10.18255/1818-1015-2017-3-280-287
Abstract
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
Supporting agencies: RFBR, project No 15-01-04619
About the Author
Vera A. Beloshapko
Lomonosov Moscow State University
Russian Federation
Russian Federation
graduate student.
1 Leninskiye Gory, Moscow 119991
References
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Review
For citations:
Beloshapko V.A. Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer. Modeling and Analysis of Information Systems. 2017;24(3):280-287. (In Russ.) https://doi.org/10.18255/1818-1015-2017-3-280-287
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