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The Riemannian wave equationwith linear lower order termand unspecified behavior of the nonlinear feedback is considered. Using themethod in [LT] 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 off is also discussed. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study, under a suitable geometric conditions, the indirect boundary stabilization for coupled Schr #x00F6;dinger equations with variable coefficients and one Dirichlet boundary feedback. The polynomial energy decay rate for smooth solutions is obtained by the combination of the Riemannian geometry method in [Ya1] and the ideas of I. Lasiecka and R. Triggiani in [LT3] . [ABSTRACT FROM AUTHOR]