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Stabilization of a nonlinear Kirchhoff equation by boundary feedback control

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Abstract

This paper is concerned with stabilization of an axially moving Kirchhoff string by boundary feedback control. We derive a nonlinear system describing transverse oscillation of the string using Hamilton’s principle and prove exponential stabilization of the system by the direct Lyapunov method. The result shows that oscillation of a nonlinear axially moving Kirchhoff string can be suppressed by a new type of boundary feedback control.

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Authors and Affiliations

  1. Department of Mathematics, Pusan National University, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 609-735, South Korea

    Daewook Kim, Gyu Ra Ko & Il Hyo Jung

  2. Institute of Liberal Education, Catholic University of Daegu, 13-13 Hayang-ro, Hayang-eup, Gyeongsan-si, Gyeongsangbuk-do, 712-702, South Korea

    Yong Han Kang

  3. Fisheries Resources and Environment Division, East Sea Fisheries Research Institute, Gangneung-si, Gangwon-do, 210-861, South Korea

    Jae Bong Lee

Authors
  1. Daewook Kim
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  2. Yong Han Kang
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  3. Jae Bong Lee
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  4. Gyu Ra Ko
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  5. Il Hyo Jung
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Correspondence to Il Hyo Jung.

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Kim, D., Kang, Y.H., Lee, J.B. et al. Stabilization of a nonlinear Kirchhoff equation by boundary feedback control. J Eng Math 77, 197–209 (2012). https://doi.org/10.1007/s10665-012-9547-z

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  • DOI: https://doi.org/10.1007/s10665-012-9547-z

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