Geodesic
Nonlocal inverse problem for determining the unknown coefficient in the beam vibration equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 60-73

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The article is devoted to the study of the direct problem for the oscillation of a homogeneous beam of finite length with non-local time conditions. Necessary and sufficient conditions for the existence of a solution to the direct problem are obtained. For the direct problem, we study the inverse problem of determining the time-dependent coefficient at the lowest derivative. Using eigenvalues and eigenfunctions, the problem is reduced to a system of integral equations. With the help of the Banach principle, the existence and uniqueness of the solution of inverse problems are shown.
Keywords: inverse problem, redefinition condition, eigenfunctions, uniqueness.
Mots-clés : non-local conditions, beam oscillations, existence 
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     author = {U. D. Durdiev and Z. R. Bozorov},
     title = {Nonlocal inverse problem for determining the unknown coefficient in the beam vibration equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {60--73},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a5/}
}
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U. D. Durdiev; Z. R. Bozorov. Nonlocal inverse problem for determining the unknown coefficient in the beam vibration equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 60-73. http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a5/