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Exponential stability of axially moving Kirchhoff-beam systems with nonlinear boundary damping and disturbance

  • * Corresponding author: Yi Cheng

    * Corresponding author: Yi Cheng 

This work were partially supported by Natural Science Foundation of Liaoning Province (No. 2020-MS-290), Liaoning Natural Fund Guidance Plan (No. 2019-ZD-0508) and Young Science and Technology Talents "Nursery Seedling" Project of Liaoning Provincial Department of Education (No, LQ2019008)

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  • This paper examines the stabilization problem of the axially moving Kirchhoff beam. Under the nonlinear damping criterion established by the slope-restricted condition, the existence and uniqueness of solutions of the closed-loop system equipped with nonlinear time-delay disturbance at the boundary is investigated via the Faedo-Galerkin approximation method. Furthermore, the solution is continuously dependent on initial conditions. Then the exponential stability of the closed-loop system is established by the direct Lyapunov method, where a novel energy function is constructed.

    Mathematics Subject Classification: Primary: 45K05, 35B45, 93B52; Secondary: 35Q93, 93D15.


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