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

2024/08/28 by Victor H. Gonzalez Martinez, Martinez, Victor Hugo Gonzalez, Juan Ricardo Muñoz +1
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum chaos and dynamical systems #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2408.15705

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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