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Indirect Internal Controllability of Weakly Coupled Degenerate Wave Equations

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Abstract

This article is devoted to the study of the exact controllability for a system of weakly coupled one dimensional degenerate wave equations. An internal locally control acts on only one equation. We show that, when the coupling parameter which depends on the degree of degradation is sufficiently small, the observation of the velocity of the first component of the solution on a left neighborhood of \(x=1\) allow us to get back a weakened energy of initial data of the second component of the solution for a sufficiently large time \(T\). Using the Hilbert Uniqueness Method, we then establish an indirect exact controllability result.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11671240), by the National Natural Science Foundation of China for the Youth (No. 12001343), by the National Natural Science Foundation of Shanxi Province (No. 201901D111042) and by the Technical Innovation Team of Jinzhong University (No. 202111).

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Authors and Affiliations

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

    Jinyan Bai, Shugen Chai & Zhiling Guo

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

    Jinyan Bai

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  1. Jinyan Bai
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  2. Shugen Chai
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  3. Zhiling Guo
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Correspondence to Shugen Chai.

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This work was supported by the National Natural Science Foundation of China (No. 11671240), by the National Natural Science Foundation of China for the Youth (No. 12001343), by the National Natural Science Foundation of Shanxi Province (No. 201901D111042) and by the Technical Innovation Team of Jinzhong University (No. 202111).

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Bai, J., Chai, S. & Guo, Z. Indirect Internal Controllability of Weakly Coupled Degenerate Wave Equations. Acta Appl Math 180, 7 (2022). https://doi.org/10.1007/s10440-022-00507-9

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  • DOI: https://doi.org/10.1007/s10440-022-00507-9

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