An inverse problem of identifying an unknown coefficient in a plate vibration equation

We consider the direct initial–boundary value problem for the equation of transverse vibrations of a thin homogeneous rectangular plate. We also study the inverse problem of determining a time-dependent plate stiffness coefficient from an additional integral overdetermination condition. Using the eigenvalues and eigenfunctions of the corresponding plate vibration operator, we reduce both the direct and inverse problems to integral equations. The existence and uniqueness of the solution to the inverse problem are established by Banach’s contraction mapping principle.

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