Stabilization of the wave equation withinterior input delay and mixed Neumann-Dirichlet boundary

Yanni  Guo; Genqi  Xu; Yansha  Guo

doi:10.3934/dcdsb.2016057

Article Contents

2016, Volume 21, Issue 8: 2491-2507. Doi: 10.3934/dcdsb.2016057

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Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary

1.
College of Science, Civil Aviation University of China, Tianjin 300300
2.
Department of Mathematics, Tianjin University, Tianjin 300072

Received: October 2015

Revised: April 2016

Published: October 2016

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Abstract

This paper considers the stabilization of a wave equation with interior input delay: $\mu_1u(x,t)+\mu_2u(x,t-\tau)$, where $u(x,t)$ is the control input. A new dynamic feedback control law is obtained to stabilize the closed-loop system exponentially for any time delay $\tau>0$ provided that $|\mu_1|\neq|\mu_2|$. Moreover, some sufficient conditions are given for discriminating the asymptotic stability and instability of the closed-loop system.

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Mathematics Subject Classification: Primary: 35B35, 93D15; Secondary: 93C20.

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