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Open Access Research

Exponential and polynomial stabilization of the Kirchhoff string by nonlinear boundary control

Yuhu Wu1* and Jianmin Wang2

Author Affiliations

1 Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, P.R. China

2 Department of Electronics Science and Technology, Harbin University of Science and Technology, Harbin, 150080, P.R. China

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Boundary Value Problems 2013, 2013:215  doi:10.1186/1687-2770-2013-215

Published: 21 October 2013

Abstract

This paper addresses the stabilization problem of the nonlinear Kirchhoff string using nonlinear boundary control. Nonlinear boundary control is the negative feedback of the transverse velocity of the string at one end, which satisfies a polynomial-type constraint. Employing the multiplier method, we establish explicit exponential and polynomial stability for the Kirchhoff string. The theoretical results are assured by numerical results of the asymptotic behavior for the system.