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

Yi Cheng; Zhihui Dong; Donal O' Regan

doi:10.3934/dcdsb.2021230

Article Contents

2022, Volume 27, Issue 8: 4331-4346. Doi: 10.3934/dcdsb.2021230

This issue Previous Article Global weak solutions to the generalized mCH equation via characteristics Next Article Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system

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

1.
School of Mathematical Sciences, Bohai University, Jinzhou 121013, China
2.
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

^* Corresponding author: Yi Cheng
^* Corresponding author: Yi Cheng

Received: February 28, 2021

Revised: June 30, 2021

Early access: September 2021

Published: August 2022

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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Abstract

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.

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

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