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Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1027–1041 | Cite as

Null controllability of some degenerate wave equations

  • Muming Zhang
  • Hang GaoEmail author
Article

Abstract

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.

Keywords

Controllability degenerate wave equation Fourier expansion observability 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNortheast Normal UniversityChangchunChina

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