Energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time-varying delay in the boundary feedback

2015 ◽  
Vol 112 ◽  
pp. 105-117 ◽  
Author(s):  
Jing Li ◽  
Shugen Chai
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Variable Coefficients ◽  
Time Varying ◽  
Acoustic Boundary Conditions ◽  
Time Varying Delay ◽  
Boundary Feedback ◽  
Varying Delay

scholarly journals Stabilization of the Wave Equation with Boundary Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hao Li ◽  
Changsong Lin ◽  
Shupeng Wang ◽  
Yanmei Zhang
Keyword(s):  
Wave Equation ◽  
Closed Loop ◽  
Nonlinear Boundary ◽  
Variable Coefficients ◽  
Time Varying ◽  
Closed Loop System ◽  
Weakly Nonlinear ◽  
Delay Term ◽  
Time Varying Delay ◽  
Varying Delay

We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.

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