Inverse Problem of Determining the Unknown Coefficient in the Beam Vibration Equation in an Infinite Domain

Annotatsiya

For the equation of transverse vibrations of a homogeneous beam, we consider the direct initial value problem in an infinite domain and study the inverse problem of determining the time-dependent beam stiffness coefficient. The solution of the direct problem is given with the help of fundamental solutions, and the existence and uniqueness of this solution are proved. Stability estimates are obtained for the solution of the inverse problem. Existence and uniqueness theorems for the solution of the inverse problem are proved using Banach’s contraction mapping principle.

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DOI

10.31857/s0374064123040039

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