Chinese Annals of Mathematics, Series B

, Volume 38, Issue 2, pp 473–488 | Cite as

Exact boundary controllability for a coupled system of wave equations with Neumann boundary controls

  • Tatsien LiEmail author
  • Bopeng Rao


This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next, in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown.


Compactness-uniqueness perturbation Boundary observability Exact boundary controllability Non-exact boundary controllability Coupled system of wave equations Neumann boundary condition 

2000 MR Subject Classification

93B05 93B07 93C20 35L53 


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Part of the work was done during the visit of the second author at the Laboratoire International Associé Sino-Français de Mathématiques Appliquées (LIASFMA) and the School of Mathematical Sciences of Fudan University during June–August 2014. He would like to thank their hospitality and support.

The authors are very grateful to Professor Xu Zhang for bringing their attention to the references [11, 12] and for the valuable discussions on several occasions, and would like also to thank the referees for their very valuable comments and remarks, which were greatly appreciated to improve the presentation of the paper.


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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina
  2. 2.Shanghai Key Laboratory for Contemporary Applied MathematicsFudan UniversityShanghaiChina
  3. 3.Nonlinear Mathematical Modeling and Methods LaboratoryFudan UniversityShanghaiChina
  4. 4.Institut de Recherche Mathématique AvancéeUniversité de StrasbourgStrasbourgFrance

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