Boundary feedback stabilization of a Schrdinger equation interconnected with a heat equation

摘要

In this paper,we study stabilization for a Schrdinger equation,which is interconnected with a heat equation via boundary coupling.A direct boundary feedback control is adopted.By a detailed spectral analysis,it is found that there are two branches of eigenvalues:one is along the negative real axis,and the other is approaching to a vertical line,which is parallel to the imagine axis.Moreover,it is shown that there is a set of generalized eigenfunctions,which forms a Riesz basis for the energy state space.Finally,the spectrum-determined growth condition is held and the exponential stability of the system is then concluded.