Uniform stabilization of the Riemannian wave equation with linear lower order term

Abstract

The Riemannian wave equation with linear lower order term and unspecified behavior of the nonlinear feedback $f$ is considered. Using the method in $ \left[ LT\right] $ we prove that the energy of the solution decays faster than the solution of some associated differential equation. The decay rate of a general second order hyperbolic equation with polynomial growth at the origin of $f$ is also discussed.