Solution of a Singularly Perturbed Mixed Problem on the Half-Line for a Parabolic Equation with a Strong Turning Point of the Limit Operator
- Autores: Eliseev A.1, Ratnikova T.1, Shaposhnikova D.1
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Afiliações:
- National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia
- Edição: Volume 59, Nº 8 (2023)
- Páginas: 1029-1045
- Seção: Articles
- URL: https://journals.rcsi.science/0374-0641/article/view/141748
- DOI: https://doi.org/10.31857/S0374064123080034
- EDN: https://elibrary.ru/INDIPZ
- ID: 141748
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Resumo
We study singularly perturbed problems in the presence of spectral singularities of the limit operator using S.A. Lomov’s regularization method. In particular, a regularized asymptotic solution is constructed for a singularly perturbed inhomogeneous mixed problem on the half-line for a parabolic equation with a strong turning point of the limit operator. Based on the idea of asymptotic integration of problems with unstable spectrum, it is shown how regularizing functions and additional regularizing operators should be introduced, the formalism of the regularization method for this type of singularity is described in detail, this algorithm is justified, and an asymptotic solution of any order in a small parameter is constructed.
Sobre autores
A. Eliseev
National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia
Email: predikat@bk.ru
Москва, Россия
T. Ratnikova
National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia
Email: ratnikovata@mpei.ru
Москва, Россия
D. Shaposhnikova
National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia
Autor responsável pela correspondência
Email: shaposhnikovda@mpei.ru
Москва, Россия
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