Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine

A. Bobodzhanov, B. Kalimbetov, N. Pardaeva
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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 slowly varying kernel. Earlier, singularly perturbed differential and integro-differential equations with rapidly oscillating coefficients were considered. The main goal of this work is to generalize the Lomov's regularization method and to identify the rapidly oscillating right-hand side to the asymptotics of the solution to the original problem.
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具有快速振荡余弦的积分微分方程正则化渐近解的构造
在本文中,我们考虑了一个具有快速振荡右手边的奇摄动积分微分方程,该方程包括一个具有慢变核的积分算子。早先,考虑了具有快速振荡系数的奇摄动微分方程和积分微分方程。这项工作的主要目标是推广Lomov正则化方法,并识别原始问题解的渐近性的快速振荡右手边。
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CiteScore
3.10
自引率
4.00%
发文量
77
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