Exponential decay domain of energy for wave equation under feedback control (Q1864202)

The authors consider the wave equation with homogeneous Dirichlet conditions on a part of the boundary and with the feedback \({\partial u}/{\partial \nu}=-(Lu+Ku')\) on the other part of the boundary. They show that the energy decays exponentially if the feedback parameters are in some domain. An estimate of the energy exponential decay in terms of the feedback parameters is obtained. The case with both distributed and boundary feedbacks is also considered. The proof is based on a multipliers method.