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Abstract <p>This article considers the well-posedness of one linear inverse problem for the three-dimensional Chaplygin equation in an unbounded parallelepiped. For this problem, the methods of ‘‘<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8411_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon\)</EquationSource> <!--LobJMat2560903Dzhamalov-m1--> </InlineEquation>-regularization’’, apriori estimates, and successive approximations with the Fourier transform are used to prove the existence and uniqueness theorems of a generalized solution to one linear inverse problem with a semi-periodic boundary condition in an anisotropic Sobolev space.</p>

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On a Linear Inverse Problem with Semi-Periodic Boundary Conditions for Three-Dimensional Chaplygin Equation in an Unbounded Parallelepiped

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • S. Z. Dzhamalov,
  • Kh. Sh. Turakulov

摘要

Abstract

This article considers the well-posedness of one linear inverse problem for the three-dimensional Chaplygin equation in an unbounded parallelepiped. For this problem, the methods of ‘‘ \(\varepsilon\) -regularization’’, apriori estimates, and successive approximations with the Fourier transform are used to prove the existence and uniqueness theorems of a generalized solution to one linear inverse problem with a semi-periodic boundary condition in an anisotropic Sobolev space.