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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-30 DOI:10.1016/j.nonrwa.2024.104122

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

引用次数: 0

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, 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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关于具有时变延迟的 KdV-KdV 系统的边界稳定问题

本文研究了 Boussinesq KdV-KdV 型系统的边界稳定问题。本文设计了由阻尼机制和延迟项的线性组合组成的适当边界反馈定律。然后，考虑到时变延迟反馈以及对空间域长度和初始数据的小限制，我们证明了所考虑的问题是很好解决的。证明结合了加藤方法和定点论证。最后，我们利用 Lyapunov 方法证明了线性化 KdV-KdV 系统的能量呈指数衰减。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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