scholarly journals Uniform stabilization of a wave equation with partial Dirichlet delayed control

2020 ◽  
Vol 9 (2) ◽  
pp. 509-533
Author(s):  
Xiaorui Wang ◽  
◽  
Genqi Xu ◽  
Keyword(s):  
Wave Equation ◽  
Uniform Stabilization

scholarly journals The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics

1996 ◽  
Vol 1 (2) ◽  
pp. 203-217 ◽  
Author(s):  
George Avalos
Keyword(s):  
Wave Equation ◽  
Feedback Control ◽  
Exponential Stability ◽  
Parabolic System ◽  
Hyperbolic Equations ◽  
Coupled System ◽  
Beam Equation ◽  
Structural Acoustics ◽  
Uniform Stabilization ◽  
Structure Interaction

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domainΩ, coupled to a “parabolic–like” beam equation holding on∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic equations.

Uniform stabilization of 1-d wave equation with anti-damping and delayed control

2020 ◽  
Vol 357 (17) ◽  
pp. 12473-12494
Author(s):  
Li Zhang ◽  
Gen Qi Xu ◽  
Hao Chen
Keyword(s):  
Wave Equation ◽  
Uniform Stabilization ◽  
D Wave
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