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Asymptotics of the Solution of a Singularly Perturbed System of Equations with a Single-Scale Internal Layerстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 17 апреля 2024 г.
- Автор: Simakov R.E.
- Журнал: Differential Equations
- Том: 59
- Номер: 3
- Год издания: 2023
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 332
- Последняя страница: 350
- DOI: 10.1134/s0012266123030047
- Аннотация: We consider a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations with different powers of the small parameter multiplying the second derivatives. A specific feature of the problem is that one of the two equations of the degenerate system has a double root and the other has three nonintersecting simple roots. It is proved that for sufficiently small values of the small parameter the problem has a solution that has a fast transition in a neighborhood of some interior point of the interval. A complete asymptotic expansion of this solution is constructed and justified. It qualitatively differs from the well-known expansion in the case where all the roots of the degenerate equations are simple but also does not coincide with the expansions in the previously studied problems with double roots; in particular, the inner transition layer turns out to be single-scale.
- Добавил в систему: Симаков Роман Евгеньевич