Boundary Feedback Stabilization of a Vibrating String with an Interior Point Mass

We study the boundary feedback stabilization for a one-dimensional wave equation with an interior point mass. We show that if the initial data belong to a certain invariant subspace of the semigroup of operators that generates the solution of the system, then the energy will decay like C=time. This improves a result of Hansen and Zuazua [1] who consider decay of solutions belonging to the domain of a power of the in¯nitesimal generator of the semigroup. 1 Introduction. In this paper we study the boundary feedback stabilization for a one-dimensional wave equation with an interior point mass. We show that if the initial data belong to a certain invariant subspace of the semigroup of operators that generates the solution of the system, then the energy will decay like C=time. This improves a result of Hansen and Zuazua [1