scholarly journals Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $H^2$-lyapunov function

2017 ◽  
Vol 7 (3) ◽  
pp. 419-448 ◽  
Author(s):  
Martin Gugat ◽  
◽  
Günter Leugering ◽  
Ke Wang ◽  
Keyword(s):  
Wave Equation ◽  
Lyapunov Function ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Neumann Boundary ◽  
Feedback Stabilization ◽  
Boundary Feedback

scholarly journals A New Approach to the Stabilization of the Wave Equation with Boundary Damping Control

2004 ◽  
Vol 9 ◽  
pp. 33 ◽  
Author(s):  
Boumediène Chentouf ◽  
Mohamed S. Boudellioua
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Neumann Boundary ◽  
Feedback Stabilization ◽  
Damping Term ◽  
New Approach ◽  
Boundary Damping ◽  
Boundary Feedback ◽  
Damping Control ◽  
New Energy

This paper deals with boundary feedback stabilization of a system, which consists of a wave equation in a bounded domain of , with Neumann boundary conditions. To stabilize the system, we propose a boundary feedback law involving only a damping term. Then using a new energy function, we show that the solutions of the system asymptotically converge to a stationary position, which depends on the initial data. Similar results were announced without proof in (Chentouf and Boudellioua, 2004).  

On the global existence and asymptotic behavior of the solution of a nonlinear wave equation with past history

2021 ◽  
Vol 62 (3) ◽  
pp. 031512
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Mohammad Kafini ◽  
Shadi Al-Omari
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Past History
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