Reconstruction of controls in hyperbolic systems by Tikhonov's method with nonsmooth stabilizers

The problem of reconstructing unknown controls in hyperbolic systems by the results of approximate observations of the motions of these systems is considered. To solve the problem, Tikhonovs method with a stabilizer containing the total time variation of the control is used. The use of such nondifferentiable stabilizer allows us to obtain more precise results in some cases than the approximation of the desired control in Lebesgue spaces. In particular, this method provides the piecewise uniform convergence of regularized approximations and makes possible the numerical reconstruction of the subtle structure of the desired control.