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arXiv · 2408.15705

Feedback boundary stabilization for the Hirota-Satsuma system with time-delay

Victor Hugo Gonzalez Martinez·Juan Ricardo Muñoz
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Abstract

This work investigates the boundary stabilization problem of the Hirota-Satsuma system. In the problem under consideration, a boundary feedback law consisting of a linear combination of a damping mechanism and a time-delay term is designed. The study shows that, with time delay feedback and a smallness restriction on the size of the initial data the energy of the Hirota-Satsuma system decays exponentially by employing two approaches: the Lyapunov method and an observability inequality combined with a contradiction argument.

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Victor Hugo Gonzalez Martinez, Juan Ricardo Muñoz. 2024-08-28. Feedback boundary stabilization for the Hirota-Satsuma system with time-delay. https://arxiv.org/abs/2408.15705

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