Stabilization of the Interconnected Schrodinger and Wave Equations with only Boundary Control at the Wave Equation

Jun Min Wang, Fei Wang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

In this paper, we consider the boundary stabilization of an interconnected system of the Schrodinger and wave equations, where the control is only proposed at the one end of the wave and the another end is interconnected with the Schrodinger. There is no control fixed on the Schrodinger and its vibration is suppressed only through boundary transmission between the wave and Schrodinger. Boundary velocity of the wave is designed to stabilize the whole system. We show that the whole system is well-posed. By a spectral analysis, Riesz basis property of the whole system is verified and hence the spectrum growth condition is then held. Therefore the exponential stability of the whole system is established. Finally the numerical computation is presented for the distributions of the spectrum of the whole system, and it is found that the spectrum of the Schrodinger depends largely both on the interconnected transmission parameter and the decay of the wave equation.

Original languageEnglish
Title of host publicationProceedings of the 37th Chinese Control Conference, CCC 2018
EditorsXin Chen, Qianchuan Zhao
PublisherIEEE Computer Society
Pages1208-1213
Number of pages6
ISBN (Electronic)9789881563941
DOIs
Publication statusPublished - 5 Oct 2018
Event37th Chinese Control Conference, CCC 2018 - Wuhan, China
Duration: 25 Jul 201827 Jul 2018

Publication series

NameChinese Control Conference, CCC
Volume2018-July
ISSN (Print)1934-1768
ISSN (Electronic)2161-2927

Conference

Conference37th Chinese Control Conference, CCC 2018
Country/TerritoryChina
CityWuhan
Period25/07/1827/07/18

Keywords

  • Boundary control
  • Schrodinger equation
  • Spectral analysis
  • Stabilization
  • Wave equation

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