Local feedback stabilisation to a non-stationary solution for a damped   non-linear wave equation
  We study a damped semi-linear wave equation in a bounded domain with smooth boundary. It is proved that any sufficiently smooth solution can be stabilised locally by a finite-dimensional feedback control supported by a given open subset satisfying a geometric condition. The proof is based on an investigation of the linearised equation, for which we construct a stabilising control satisfying the required properties. We next prove that the same control stabilises locally the non-linear problem. 
Ka\"is Ammari (FSM), Thomas Duyckaerts (LAGA), Armen Shirikyan (AGM)
math.OC math.AP