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arXiv · 2305.15532

On the boundary stabilization of the KdV-KdV system with time-dependent delay

Roberto de A. Capistrano-Filho·Boumediène Chentouf·Victor H. Gonzalez Martinez·Juan Ricardo Muñoz
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Abstract

The boundary stabilization problem of the Boussinesq KdV-KdV type system is investigated in this paper. An appropriate boundary feedback law consisting of a linear combination of a damping mechanism and a delay term is designed. Then, first, considering time-varying delay feedback together with a smallness restriction on the length of the spatial domain and the initial data, we show that the problem under consideration is well-posed. The proof combines Kato's approach and the fixed-point argument. Last but not least, we prove that the energy of the linearized KdV-KdV system decays exponentially by employing the Lyapunov method.

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Roberto de A. Capistrano-Filho, Boumediène Chentouf, Victor H. Gonzalez Martinez, Juan Ricardo Muñoz. 2023-05-24. On the boundary stabilization of the KdV-KdV system with time-dependent delay. https://doi.org/10.1016/j.nonrwa2024.104122

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