Stabilization of systems governed by the wave equation in the presence of distributed white noise

It is shown that by application of velocity feedback systems governed by the wave equation perturbed by distributed white noise can be stabilized with respect to a ball centered at the origin in the energy space. The radius of this attractor depends on the noise strength and the damping. It is further shown that by approriate choice of damping, it is possible to minimize the size of the attractor (i.e., reduced vibration amplitude) and maximize the decay rate.