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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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2016-10-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/385 |
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| author | V. F. Butuzov V. A. Beloshapko |
| author_facet | V. F. Butuzov V. A. Beloshapko |
| author_sort | V. F. Butuzov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ddbc45e4b8da4baeadce046edcf8f63e |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2016-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-ddbc45e4b8da4baeadce046edcf8f63e2025-08-20T03:22:03ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172016-10-0123551552810.18255/1818-1015-2016-5-515-528321Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate EquationV. F. Butuzov0V. A. Beloshapko1Lomonosov Moscow State University, GSP-1, 1-2 Leninskiye Gory, 119991, RussiaLomonosov Moscow State University, GSP-1, 1-2 Leninskiye Gory, 119991, RussiaA 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.https://www.mais-journal.ru/jour/article/view/385singularly perturbed elliptic equationcase of multiple root of the degenerate equationasymptotic expansion of boundary layer type solutionthree-band boundary layer |
| spellingShingle | V. F. Butuzov V. A. Beloshapko Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation Моделирование и анализ информационных систем singularly perturbed elliptic equation case of multiple root of the degenerate equation asymptotic expansion of boundary layer type solution three-band boundary layer |
| title | Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation |
| title_full | Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation |
| title_fullStr | Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation |
| title_full_unstemmed | Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation |
| title_short | Singularly Perturbed Elliptic Dirichlet Problem with a Multiple Root of the Degenerate Equation |
| title_sort | singularly perturbed elliptic dirichlet problem with a multiple root of the degenerate equation |
| topic | singularly perturbed elliptic equation case of multiple root of the degenerate equation asymptotic expansion of boundary layer type solution three-band boundary layer |
| url | https://www.mais-journal.ru/jour/article/view/385 |
| work_keys_str_mv | AT vfbutuzov singularlyperturbedellipticdirichletproblemwithamultiplerootofthedegenerateequation AT vabeloshapko singularlyperturbedellipticdirichletproblemwithamultiplerootofthedegenerateequation |