Email this article 
AVERAGING OF INTEGRO-DIFFERENTIAL SYSTEMS OF EQUATIONS WITH MULTIPOINT BOUNDARY CONDITIONS CONDITIONS
- Authors: Levenshtam V.B.1,2,3, Yavaeva M.R.1
-
Affiliations:
- Southern Federal University
- Gubkin Mathematical Institute named after V. L. Steklov RAS (V. L. Steklov Mathematical Institute Russian Academy of Sciences)
- Southern Mathematical Institute - Branch of the All-Russian Scientific Center of RAS
- Issue: Vol 65, No 5 (2025)
- Pages: 665-672
- Section: Partial Differential Equations
- URL: https://bulletin.ssaa.ru/0044-4669/article/view/686924
- DOI: https://doi.org/10.31857/S0044466925050057
- EDN: https://elibrary.ru/IGDKCA
- ID: 686924
Cite item
Open Access
Access granted
Subscription Access
Abstract
In this paper we consider a system of integro-differential equations with rapidly time oscillating data and multipoint integral boundary conditions. The latter may depend explicitly on a large parameter ω — high frequency of oscillations of the initial system of equations. For this problem the limit problem at ω → ∞is constructed and the limit transition is justified. Thereby, the time averaging method, which is also called the Krylov–Bogoliubov averaging method, is justified for the above problem in this paper.
About the authors
V. B. Levenshtam
Southern Federal University; Gubkin Mathematical Institute named after V. L. Steklov RAS (V. L. Steklov Mathematical Institute Russian Academy of Sciences); Southern Mathematical Institute - Branch of the All-Russian Scientific Center of RAS
Email: vlevenshtam@yandex.ru
Rostov-on-Don, Russia; Moscow, Russia; Vladikavkaz, Russia
M. R. Yavaeva
Southern Federal University
Email: marinayavaeva@yandex.ru
Rostov-on-Don, Russia
References
- Боголюбов Н.Н. О некоторых статистических методах в математической физике. Киев: Изд. АН УССР, 1945.
- Боголюбов Н.Н., Митропольский Н.М. Асимптотические методы в теории нелинейных колебаний. М.: Наука, 1974.
- Константинов М.М., Байнов Д.Д. О применении метода усреднения к некоторым многоточечным краевым задачам // Bull. Math. da la Soc. Sci. Math. de la R. S. de la Roumanie. 1974. Т. 18(66).№3/4. С. 307–310.
- Левенштам В.Б., Шубин П.Е. Обоснование метода усреднения для дифференциальных уравнений с большими быстро осциллирующими слагаемыми и краевыми условиями // Матем. заметки. 2016. Т. 100. Вып. 1. С. 94–108.
- Bigirindavyi D., Levenshtam V.B. Justification of the averaging method for differential equations with multipoint boundary value problems // Springer Proceedings in Mathematics and Statistics. 2021. Vol. 357. P. 137–142.
- Симоненко И.Б. Обоснование метода осреднения для абстрактных параболических уравнений // Матем. сб. 1970. Т. 81(123).№1. С. 53–61.
Supplementary files
