On eigenelements of a two-dimensional Steklov-type boundary value problem for the Lamé operator
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On eigenelements of a two-dimensional Steklov-type boundary value problem for the Lamé operator
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| Автор |
Davletov, D. B.
Davletov, O. B. Davletova, R. R. Ershov, A. A. |
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| Тематика |
BOUNDARY VALUE PROBLEM
EIGENELEMENTS LAMÉ OPERATOR STEKLOV SPECTRAL CONDITION |
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| Описание |
In this paper, we study a two-dimensional Steklov-type boundary value problem for the Lamé operator in a half-strip, which is the limiting problem for a singularly perturbed boundary-value problem in a half-strip with a small hole. A theorem on the existence of eigenelements of the boundary value problem under study is proved. In particular, we obtain estimates for the eigenvalues expressed in terms of the Lamé constants and a parameter that determines the width of the half-strip, and refine the structure of the corresponding eigenfunctions, which determines their behavior as their argument move away from the base of the half-strip. Moreover, explicit expressions for the eigenvalues of the limiting boundary value problem are found up to the solution of a system of algebraic equations. The results obtained in this paper will make it possible to construct and rigorously justify an asymptotic expansion of the eigenvalue of a singularly perturbed boundary value problem in a half-strip with a small round hole in powers of a small parameter that determines the diameter of the hole. © 2023 Udmurt State University. All rights reserved.
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| Дата |
2024-04-05T16:22:27Z
2024-04-05T16:22:27Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Давлетов, ДБ, Давлетов, ОБ, Давлетова, РР & Ершов, АА 2023, 'О СОБСТВЕННЫХ ЭЛЕМЕНТАХ ДВУМЕРНОЙ КРАЕВОЙ ЗАДАЧИ ТИПА СТЕКЛОВА ДЛЯ ОПЕРАТОРА ЛАМЭ', Вестник Удмуртского университета. Математика. Механика. Компьютерные науки, Том. 33, № 1, стр. 54-65. https://doi.org/10.35634/vm230104
Давлетов, Д. Б., Давлетов, О. Б., Давлетова, Р. Р., & Ершов, А. А. (2023). О СОБСТВЕННЫХ ЭЛЕМЕНТАХ ДВУМЕРНОЙ КРАЕВОЙ ЗАДАЧИ ТИПА СТЕКЛОВА ДЛЯ ОПЕРАТОРА ЛАМЭ. Вестник Удмуртского университета. Математика. Механика. Компьютерные науки, 33(1), 54-65. https://doi.org/10.35634/vm230104 1994-9197 Final All Open Access, Bronze https://www.scopus.com/inward/record.uri?eid=2-s2.0-85159872107&doi=10.35634%2fVM230104&partnerID=40&md5=dee4580df31337ad581ae720d72f48e3 http://vm.udsu.ru/doc/issues-2023/23-01-04.pdf http://elar.urfu.ru/handle/10995/130494 50465442 10.35634/VM230104 85159872107 001101545900004 |
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| Язык |
ru
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Udmurt State University
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| Источник |
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki
Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki |
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