Controllability Properties of a Vibrating String with Variable Axial Load Only

We show that the set of equilibrium-like states (y(d),0) of a vibrating string which can approximately be reached in the energy space H-0(1)(0, 1) x L-2(0, 1) from almost any non-zero initial datum, namely, (y(0),y(1)) is an element of (H-2(0, 1) boolean AND H-0(1)(0, 1)) x H-1(0, 1), (y(0), y(1)) not equal (0,0) by varying its axial load only is dense in the subspace H-0(1)(0, 1) x {0} of this space. This result is based on a constructive argument and makes use of piecewise constant-in-time control functions (loads) only, which enter the model equation as coefficients.