On a problem of control of oscillations of a plane membrane by a force applied to its boundary

Earlier, the problems of control of a plane membrane by a boundary force were considered by many authors (see, e.g., the review article by J.-L. Lions and references there). In the work, the problem of the full damping of initial membrane oscillations is considered and the necessary damping time is estimated. However, the author proves only existence of such control, while no explicit expressions for the control is given