Stabilization of the Schrödinger equation through boundary coupling with a heat equation

Abstract

In this paper, we study an interconnected system consisting of a Schrödinger equation and a heat equation coupled through boundary conditions. Using semigroup theory, we first establish the well-posedness of the closed-loop system. Furthermore, we prove that the dissipation induced by the heat equation is sufficient to ensure the exponential decay of the solution. The proof relies on a frequency domain approach from semigroup theory, combining a contradiction argument with multiplier techniques to perform a detailed analysis of the resolvent operator.