ESTIMATES FOR THE CONTROLS OF THE WAVE EQUATION WITH A POTENTIAL

This article studies the L-2 -norm of the boundary controls for the one dimensional linear wave equation with a space variable potential a = a(x). It is known these controls depend on a and their norms may increase exponentially with parallel to a parallel to L-infinity . Our aim is to make a deeper study of this dependence in correlation with the properties of the initial data. The main result of the paper shows that the minimal L-2 -norm controls are uniformly bounded with respect to the potential a, if the initial data have only sufficiently high eigenmodes.