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Null controllability of some degenerate wave equations

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Muming Zhang & Hang Gao

Authors
  1. Muming Zhang
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  2. Hang Gao
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Corresponding author

Correspondence to Hang Gao.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11371084, 11471070 and 11171060, by the Fundamental Research Funds for the Central Universities under Grant Nos. 14ZZ2222 and 2412015BJ011, by the National Basic Research Program of China (973 Program) under Grant No. 2011CB808002, and by the Fok Ying Tong Education Foundation under Grant No. 141001.

This paper was recommended for publication by Editor SUN Jian.

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Zhang, M., Gao, H. Null controllability of some degenerate wave equations. J Syst Sci Complex 30, 1027–1041 (2017). https://doi.org/10.1007/s11424-016-5281-3

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  • DOI: https://doi.org/10.1007/s11424-016-5281-3

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