On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass

Ghada Ben Belgacem; Chaker Jammazi

doi:10.3934/dcdsb.2018286

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2019, Volume 24, Issue 4: 1653-1675. Doi: 10.3934/dcdsb.2018286

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On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass

Ghada Ben Belgacem^, and
Chaker Jammazi

Faculté des Sciences de Bizerte and Ecole Polytechnique de Tunisie, Laboratoire LIM d'Ingénierie Mathématique., Université de Carthage-Tunisia

* Corresponding author: Ghada Ben Belgacem
* Corresponding author: Ghada Ben Belgacem

Received: January 31, 2017

Revised: March 31, 2018

Early access: August 2018

Published: January 2019

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Abstract

In this article, the problem of finite-time stabilization of two strings connected by point mass is discussed. We use the so-called Riemann coordinates to convert the study system into four transport equations coupled with the dynamic of the charge. We act by Bhat-Bernstein feedbacks in various positions (two extremities, the point mass and one of boundaries, only on the point mass, ...) and we show that in some cases the nature of the stability depends sensitively on the physical parameters of the system.

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Mathematics Subject Classification: Primary: 35L05, 35L40; Secondary: 93C20, 93D15.

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Figure 1. Vibrating strings attached with a point mass [34]

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