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Exact Controllability of Wave Equations with Interior Degeneracy and One-Sided Boundary Control

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Abstract

In this paper, the authors mainly consider the exact controllability for degenerate wave equation, which degenerates at the interior point, and boundary controls acting at only one of the boundary points. The main results are that, it is possible to control both the position and the velocity at every point of the body and at a certain time T for the wave equation with interior weakly degeneracy. Moreover, it is shown that the exact controllability fails for the wave equation with interior strongly degeneracy. In order to steer the system to a certain state, one needs controls to act on both boundary points for the wave equation with interior strongly degeneracy. The difficulties are addressed by means of spectral analysis.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China

    Jinyan Bai & Shugen Chai

  2. School of Mathematics, Jinzhong University, Jinzhong, 030619, China

    Jinyan Bai

Authors
  1. Jinyan Bai
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  2. Shugen Chai
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Corresponding author

Correspondence to Shugen Chai.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 12271316, the National Natural Science Foundation of China for the Youth under Grant No. 11801339, Shanxi Sciences Project for Selected Overseas Scholars under Grant No. 2018–172, and the Technical Innovation Team of Jinzhong University under Grant No. 202111.

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Bai, J., Chai, S. Exact Controllability of Wave Equations with Interior Degeneracy and One-Sided Boundary Control. J Syst Sci Complex 36, 656–671 (2023). https://doi.org/10.1007/s11424-023-1094-3

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  • DOI: https://doi.org/10.1007/s11424-023-1094-3

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