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Nonlocal Inverse Problem for Determining the Unknown Coefficient in the Beam Vibration Equation

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Abstract

The paper is devoted to the study of the direct problem for the vibration of a homogeneous beam of finite length with nonlocal time conditions. Necessary and sufficient conditions for the existence of a solution of the direct problem are obtained. For the direct problem, we study the inverse problem of determining the time-dependent coefficient multiplying a lower-order derivative. Using the eigenvalues and eigenfunctions, the problem is reduced to a system of integral equations. The existence and uniqueness of the solution of inverse problems are shown using the Banach principle.

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Funding

This work was supported by the Ministry of Education and Science of the Russian Federation, agreement no. 075-02-2022-890.

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Authors and Affiliations

  1. Bukhara State University, Bukhara, 200114, Uzbekistan

    U. D. Durdiev

  2. Bukhara Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Bukhara, 200117, Uzbekistan

    U. D. Durdiev & Z. R. Bozorov

Authors
  1. U. D. Durdiev
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  2. Z. R. Bozorov
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Correspondence to U. D. Durdiev or Z. R. Bozorov.

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Translated by V. Potapchouck

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Durdiev, U.D., Bozorov, Z.R. Nonlocal Inverse Problem for Determining the Unknown Coefficient in the Beam Vibration Equation. J. Appl. Ind. Math. 17, 281–290 (2023). https://doi.org/10.1134/S1990478923020060

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