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Abstract <p>The paper considers a system of integro-differential equations with data rapidly oscillating over time and multipoint integral boundary conditions. The latter can explicitly depend on a large parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2228_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \)</EquationSource> <!--ComMat2570028Levenshtam-m1--> </InlineEquation>—a high oscillation frequency of the original system of equations. For this problem, a limit problem at <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2228_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \to \infty \)</EquationSource> <!--ComMat2570028Levenshtam-m2--> </InlineEquation> is constructed and the passage to the limit is substantiated. Thus, for this problem, the paper justifies the method of time averaging, which is also called the Krylov–Bogolyubov averaging method.</p>

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Averaging of Systems of Integro-Differential Equations with Multipoint Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • V. B. Levenshtam,
  • M. R. Yavaeva

摘要

Abstract

The paper considers a system of integro-differential equations with data rapidly oscillating over time and multipoint integral boundary conditions. The latter can explicitly depend on a large parameter \(\omega \) —a high oscillation frequency of the original system of equations. For this problem, a limit problem at \(\omega \to \infty \) is constructed and the passage to the limit is substantiated. Thus, for this problem, the paper justifies the method of time averaging, which is also called the Krylov–Bogolyubov averaging method.