Identification of the right hand side of equation of torsional vibrations of a rod

Abstract

We analyze the solvability of the inverse problem with an unknown coefficient for a fourth-order hyperbolic equation. To investigate the solvability of the inverse problem, the problem is considered in a rectangle area, with set conditions being typical of the boundary-value problem and an auxiliary condition being necessary of the unknown coefficient searching. Using the Fourier method, the problem is reduced to solving a system of integral equations, and using the compressed mapping method, the existence and uniqueness of a solution to the system of integral equations is proved. The existence and uniqueness of a classical solution to the original problem is shown.