Estimates for normal solutions in problems with irregular zonal controls for the wave equation

For the wave equation with variable coefficients and boundary conditions of the first kind, we consider mutually dual problems with irregular zonal controls and regular zonal observations. Constructive estimates of well-posed solvability are obtained for the observation problem with strong generalized solutions on sufficiently large time intervals. These estimates contain information necessary for the construction of stable approximations to solutions of both problems with the use of the earlier suggested variational method.