Solvability of the inverse problem of external influence in the many-dimensional wave equation

The solvability of the inverse problem of finding a solution problem $u(x,t)$ and the unknown coefficients $q_{1}(t),\ldots,q_{m}(t)$ in the many-dimensional hyperbolic equation when setting the conditions for initial boundary value problem and the conditions of the overdetermination. Existence of solutions are proven.