Stability of a Schrödinger equation with internal fractional damping

Abstract

In this paper, we are concerned with the stabilization of a linear Schrödinger equation in an n-dimensional open bounded domain under Dirichlet boundary conditions with an internal fractional damping. We reformulate the system into an augmented model and prove the well-posedness of it by using semigroup method. Based on a general criteria of Arendt-Batty, we show that the system is strongly stable. By combining frequency domain method and multiplier techniques, we establish an optimal polynomial energy decay rate.