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Approximate Boundary Null Controllability and Approximate Boundary Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls

  • Tatsien LiEmail author
  • Xing Lu
  • Bopeng Rao
Chapter

Abstract

In this paper, for a coupled system of wave equations with Neumann boundary controls, the approximate boundary null controllability, the approximate boundary synchronization and the approximate boundary synchronization by groups are taken into account, respectively. Like in the case with Dirichlet boundary controls, the corresponding conditions of compatibility, and the criteria of Kalman’s type as necessary conditions are obtained. The sufficiency of Kalman’s criteria is further discussed in one dimensional space.

Notes

Acknowledgements

Projet supported by the National Basic Research Program of China (No 2013CB834100), and the National Natural Science Foundation of China (No 11121101).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

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

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