Stabilization of the water-wave equations with surface tension
  This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time, provided that the external pressure is given by the normal component of the velocity at the free surface multiplied by an appropriate cut-off function. 
Thomas Alazard
math.AP math.OC