Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer
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 diffe...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2017-06-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/518 |
| _version_ | 1797877978482343936 |
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| author | Vera A. Beloshapko |
| author_facet | Vera A. Beloshapko |
| author_sort | Vera A. Beloshapko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T02:26:30Z |
| format | Article |
| id | doaj.art-d9e2747bb5f64051a030015b62e25fa2 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:26:30Z |
| publishDate | 2017-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-d9e2747bb5f64051a030015b62e25fa22023-03-13T08:07:29ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-06-0124328028710.18255/1818-1015-2017-3-280-287368Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary LayerVera A. Beloshapko0Московский государственный университет имени М.В. ЛомоносоваAbstract. 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.https://www.mais-journal.ru/jour/article/view/518сингулярно возмущенное эллиптическое уравнениеслучай кратного корня вырожденного уравненияасимптотическое разложение решения погранслойного типатрехзонный пограничный слойоценочная функция |
| spellingShingle | Vera A. Beloshapko Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer Моделирование и анализ информационных систем сингулярно возмущенное эллиптическое уравнение случай кратного корня вырожденного уравнения асимптотическое разложение решения погранслойного типа трехзонный пограничный слой оценочная функция |
| title | Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer |
| title_full | Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer |
| title_fullStr | Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer |
| title_full_unstemmed | Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer |
| title_short | Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer |
| title_sort | singularly perturbed elliptic dirichlet problem with three band boundary layer |
| topic | сингулярно возмущенное эллиптическое уравнение случай кратного корня вырожденного уравнения асимптотическое разложение решения погранслойного типа трехзонный пограничный слой оценочная функция |
| url | https://www.mais-journal.ru/jour/article/view/518 |
| work_keys_str_mv | AT veraabeloshapko singularlyperturbedellipticdirichletproblemwiththreebandboundarylayer |