Exponential stability of 1-d wave equation with the boundary time delay based on the interior control

Yaru Xie; Genqi Xu

doi:10.3934/dcdss.2017028

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2017, Volume 10, Issue 3: 557-579. Doi: 10.3934/dcdss.2017028

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Exponential stability of 1-d wave equation with the boundary time delay based on the interior control

Yaru Xie and
Genqi Xu

Department of Mathematics, Tianjin University, Haihe Education Park, Tianjin, Tianjin 300350, China

Received: May 31, 2016

Revised: December 31, 2016

Published: May 2017

This work is supported by Science Foundation of China under Grant Nos.61174080, 61503275 and 61573252.

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Abstract

In this paper, the stability problem of 1-d wave equation with the boundary delay and the interior control is considered. The well-posedness of the closed-loop system is investigated by the linear operator. Based on the idea of Lyapunov functional technology, we give the condition on the relationship between the control parameter α and the delay parameter k to guarantee the exponential stability of the system.

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Mathematics Subject Classification: Primary: 35L05, 37L45; Secondary: 37L15.

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