Optimal location of the actuator for the pointwise stabilization of a string

We study the large time behavior of the solutions of a homogeneous string e quation with a homogeneous Dirichlet boundary condition at the left end and a homogeneous Neumann boundary condition at the right end. A pointwise int erior actuator gives a linear viscous damping term. We give a complete char acterization of the positions of the actuator for which the system becomes exponentially stable in the energy space. Moreover, we show that the fastes t decay rate is obtained if the actuator is located at the middle of the st ring. (C) 2000 Academie des sciences/Editions scientifiques et medicales El sevier SAS.