The paper investigates the boundary stabilization problem of the Hirota-Satsuma system. It designs an appropriate boundary feedback law that consists of a linear combination of a damping mechanism and a delay term. The study shows that, with time delay feedback and a smallness restriction on the size of the initial data the energy the Hirota-Satsuma system decays exponentially by employing the Lyapunov method.
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Martinez et al. (2024) studied this question.
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