Energy decay rate of wave equations with indefinite damping (Q1975458)

The authors consider the one-dimensional wave equation with an indefinite sign viscous damping and a zero order potential term. The main result of the paper asserts that if the damping coefficient is ``more positive than negative'', the energy of the solution of the considered equation satisfying a Dirichlet boundary condition decays uniformly exponentially to zero. This generalizes a previous result of Freitas and Zuazua. The proof is based on an asymptotic expansion of eigenvalues and eigenfunctions of the damped wave equation (established by using a shooting method).