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		Junjun LIU,Junmin WANG.[en_title][J].Control Theory and Technology,2013,11(4):558~562.[Copy]

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JunjunLIU,JunminWANG
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(School of Mathematics, Beijing Institute of Technology)

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Received:August 30, 2012Revised:November 02, 2012

基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 61074049, 61273130).

Boundary feedback stabilization of a Schr$\＂{o}$dinger equation interconnected with a heat equation

Junjun LIU,Junmin WANG

(School of Mathematics, Beijing Institute of Technology)

Abstract:

In this paper, we study stabilization for a Schr$\＂{o}$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.

Key words: Schr$\＂{o}$dinger equation Heat equation Boundary control Stability Riesz basis