A Time-Nonlocal Inverse Problem for the Beam Vibration Equation with an Integral Condition

Annotatsiya

We study the direct problem for transverse vibrations of a homogeneous beam of finite length with time-nonlocal conditions and obtain necessary and sufficient conditions for the existence of its solution. For the direct problem, the inverse problem of determining the time-dependent coefficients of the lower derivative and the right-hand side in the equation is studied. The existence and uniqueness of the solution of the inverse problem are proved. The solution is based on separation of variables, which is used to reduce the problems to an integral equation and a system of integral equations.

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DOI

10.1134/s0012266123030060

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