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Well-posedness and exact controllability of fourth-order Schrödinger equation with hinged boundary control and collocated observation

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Abstract

In this paper, we consider the well-posedness and exact controllability of a fourth-order multi-dimensional Schrödinger equation with hinged boundary by either moment or Dirichlet boundary control and collocated observation, respectively. It is shown that in both cases, the systems are well posed in the sense of D. Salamon, which implies that the systems are exactly controllable in some finite time interval if and only if its corresponding closed loop systems under the direct output proportional feedback are exponentially stable. This leads us to discuss further the exact controllability of the systems. In addition, the systems are consequently shown to be regular in the sense of G. Weiss as well, and the feedthrough operators are zero.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Ruili Wen, Shugen Chai & Bao-Zhu Guo

  2. Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100190, People’s Republic of China

    Bao-Zhu Guo

  3. School of Computational and Applied Mathematics, University of the Witwatersrand, Wits, Johannesburg, 2050, South Africa

    Bao-Zhu Guo

Authors
  1. Ruili Wen
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  2. Shugen Chai
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  3. Bao-Zhu Guo
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Corresponding author

Correspondence to Ruili Wen.

Additional information

This work was supported by the National Natural Science Foundation of China for the Youth (No. 61503230) and the National Natural Science Foundation of China for the Youth (No. 61403239).

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Wen, R., Chai, S. & Guo, BZ. Well-posedness and exact controllability of fourth-order Schrödinger equation with hinged boundary control and collocated observation. Math. Control Signals Syst. 28, 22 (2016). https://doi.org/10.1007/s00498-016-0175-4

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  • DOI: https://doi.org/10.1007/s00498-016-0175-4

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