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Exact Boundary Controllability of the Linear Biharmonic Schrödinger Equation with Variable Coefficients

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Abstract

In this paper, we study the exact boundary controllability of the linear fourth-order Schrödinger equation, with variable physical parameters and clamped boundary conditions on a bounded interval. The control acts on the first spatial derivative at the right endpoint. We prove that this control system is exactly controllable at any time \(T>0\). The proofs are based on a detailed spectral analysis and the use of nonharmonic Fourier series.

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Acknowledgements

The authors would like to thank the referee for valuable suggestions and comments that helped to improve the paper.

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Authors and Affiliations

  1. LR Analysis and Control of PDEs, LR22ES03, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5019, Monastir, Tunisia

    Kaïs Ammari & Hedi Bouzidi

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  1. Kaïs Ammari
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  2. Hedi Bouzidi
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Correspondence to Kaïs Ammari.

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Ammari, K., Bouzidi, H. Exact Boundary Controllability of the Linear Biharmonic Schrödinger Equation with Variable Coefficients. J Dyn Control Syst 29, 703–719 (2023). https://doi.org/10.1007/s10883-022-09609-x

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  • DOI: https://doi.org/10.1007/s10883-022-09609-x

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