Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation
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 th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2016-10-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/385 |
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| Summary: | 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. |
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| ISSN: | 1818-1015 2313-5417 |