Justification of the steepest descent method for the integral statement of an inverse problem for a hyperbolic equation

Under consideration is the steepest descent method for solving the problem of determination of a coefficient in a hyperbolic equation in integral statement. The properties of solutions to the direct and inverse problems are studied. Estimates for the objective functional and its gradient are obtained. Convergence in the mean is proved for the steepest descent method for minimizing the residual functional.