Algorithm of the Regularization Method for a Singularly Perturbed Integro-differential Equation with a Rapidly Decreasing Kernel and Rapidly Oscillating Inhomogeneity
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https://elib.sfu-kras.ru/handle/2311/145173Author:
Bobodzhanov, Abdukhafiz A.
Kalimbetov, Burkhan T.
Safonov, Valeriy F.
Бободжанов, Абдухафиз А.
Калимбетов, Бурхан Т.
Сафонов, Валерий Ф.
Date:
2022Journal Name:
Журнал Сибирского федерального университета. Математика и физика, 2022. Journal of Siberian Federal University. Mathematics & Physics, 2022, 15 (2)Abstract:
In this paper, we consider a singularly perturbed integro-differential equation with a rapidly
oscillating right-hand side, which includes an integral operator with a rapidly varying kernel. The main
goal of this work is to generalize the Lomov’s regularization method and to reveal the influence of the
rapidly oscillating right-hand side and a rapidly varying kernel on the asymptotics of the solution to the
original problem В настоящей работе рассматривается сингулярно возмущенное интегро-
дифференциальное уравнение с быстро осциллирующей правой частью, которое включает
интегральный оператор с быстро меняющимся ядром. Основная цель данной работы — обобщить
метод регуляризации Ломова и выявить влияние быстро осциллирующей правой части и быстро
меняющегося ядра на асимптотику решения исходной задачи
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