Polynomial decay for coupled Schrödinger equations with variable coefficients and damped by one Dirichlet boundary feedback

Abstract

The main purpose of this paper is to study, under a suitable geometric conditions, the indirect boundary stabilization for coupled Schrödinger 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 $\left[ Ya1\right] $ and the ideas of I. Lasiecka and R. Triggiani in $\left[ LT3\right].