scholarly journals Chaotic Vibration of the Wave Equation with Nonlinear Feedback Boundary Control: Progress and Open Questions

2004 ◽  
pp. 25-50 ◽  
Author(s):  
Goong Chen ◽  
Sze-Bi Hsu ◽  
Jianxin Zhou
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Nonlinear Feedback ◽  
Chaotic Vibration ◽  
Open Questions

scholarly journals Boundary Stabilization of a Semilinear Wave Equation with Variable Coefficients under the Time-Varying and Nonlinear Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bei Gong ◽  
Xiaopeng Zhao
Keyword(s):  
Wave Equation ◽  
Riemannian Geometry ◽  
Nonlinear Term ◽  
Variable Coefficients ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Boundary Stabilization ◽  
Semilinear Wave Equation ◽  
The Stability ◽  
Stability Results

We study the boundary stabilization of a semilinear wave equation with variable coefficients under the time-varying and nonlinear feedback. By the Riemannian geometry methods, we obtain the stability results of the system under suitable assumptions of the bound of the time-varying term and the nonlinearity of the nonlinear term.

Boundary Feedback Stabilization of a Two-Dimensional Wave Equation

2011 ◽  
Vol 219-220 ◽  
pp. 957-960
Author(s):  
Chun Li Guo ◽  
Cheng Kang Xie ◽  
Fei Shen
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Closed System ◽  
Feedback Stabilization ◽  
Two Dimensional ◽  
Backstepping Method ◽  
Boundary Feedback ◽  
Dimensional Wave

Boundary control of two-dimensional wave equation on the rectangle is considered in this paper. Boundary controllers are designed through backstepping method. Stabilization of the closed system is obtained under the controllers.

Lp-Optimal Boundary Control for the Wave Equation

2005 ◽  
Vol 44 (1) ◽  
pp. 49-74 ◽  
Author(s):  
M. Gugat ◽  
G. Leugering ◽  
G. Sklyar
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Optimal Boundary ◽  
Optimal Boundary Control
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