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Stabilizability for Quasilinear Klein–Gordon–Schrödinger System with Variable Coefficients

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Abstract

This paper concerns with the stabilizability for a quasilinear Klein–Gordon–Schrödinger system with variable coefficients in dimensionless form. The stabilizability of quaslinear Klein–Gordon-Wave system with the Kelvin–Voigt damping has been considered by Liu–Yan–Zhang (SIAM J Control Optim 61:1651–1678, 2023). Our main contribution is to find a suitable linear feedback control law such that the quasilinear Klein–Gordon–Schrödinger system is exponentially stable under certain smallness conditions.

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Acknowledgements

We are very grateful to the anonymous referees made numerous suggestions for improving the presentation. This work is supported by Guangxi science and technology department specific research project of Guangxi for research bases and talents (Guike AD23026076) and NSFC No 12161006 and Guangxi Natural Science Foundation No. 2021JJG110002.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, People’s Republic of China

    Weijia Li, Yuqi Shangguan & Weiping Yan

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  1. Weijia Li
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  2. Yuqi Shangguan
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Correspondence to Weiping Yan.

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Communicated by Enrique Zuazua.

Dedicated to Professor Vicenţiu D. Rădulescu on the occasion of his 65th birthday.

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Li, W., Shangguan, Y. & Yan, W. Stabilizability for Quasilinear Klein–Gordon–Schrödinger System with Variable Coefficients. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02445-y

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