An inverse problem with a time-nonlocal integral condition for the beam vibration equation

The paper is devoted to the study of a direct problem with time-nonlocal conditions and inverse problems with integral overdetermination conditions for the equation of transverse vibrations of a beam. Necessary and sufficient conditions for the existence of a solution of the direct problem are obtained. The inverse problem consists of recovering an unknown time-dependent coefficient from an additional integral overdetermination condition. Using the eigenvalues and eigenfunctions of the corresponding beam vibration operator, both the direct and inverse problems are reduced to integral equations. The existence and uniqueness of the solution to the inverse problem are established by Banach’s contraction mapping principle.

Hali tarjima qilinmagan