Stabilization and regularity transmission of a Schrödinger equation through boundary connections with a Kelvin‐Voigt damped beam equation

Abstract

AbstractIn this paper, we study stability for a Schrödinger equation interacted by an Euler‐Bernoulli beam equation with Kelvin‐Voigt damping through weak boundary connections. It is shown that the whole coupled system is well‐posed. With a careful spectral analysis, it is shown that the system operator of the closed‐loop system is not of compact resolvent and the spectrum consists of three branches. By means of asymptotic analysis, the asymptotic expressions of eigenfunctions are obtained. The Riesz basis property and exponential stability of the system are concluded by comparison method in Riesz basis approach. Finally, we show that the associated C0‐semigroup is of Gevery class which is a remarkable difference with the related literature.