Exponential and polynomial stabilization of the Kirchhoff string by nonlinear boundary control
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
Boundary Value Problems 2013, 2013:215 doi:10.1186/1687-2770-2013-215Published: 21 October 2013
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.