scholarly journals Remarks on exponential stability for a coupled system of elasticity and thermoelasticity with second sound

2020 ◽  
Author(s):  
Manuel Rissel ◽  
Ya-Guang Wang
Keyword(s):  
Exponential Stability ◽  
Coupled System ◽  
Second Sound

Exponential stability of a flexible structure with second sound

2019 ◽  
Vol 122 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Wenjun Liu ◽  
Jiangyong Yu ◽  
Gang Li
Keyword(s):  
Exponential Stability ◽  
Flexible Structure ◽  
Second Sound

Stability for a nonlinear coupled system of elasticity and thermoelasticity with second sound

2014 ◽  
Vol 13 (01) ◽  
pp. 45-75 ◽  
Author(s):  
Yi-Ping Meng ◽  
Ya-Guang Wang
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Middle Part ◽  
Second Sound ◽  
Qualitative Properties ◽  
Thermal Change ◽  
Nonlinear Coupled System ◽  
Initial Boundary Value

In this paper, we study the qualitative properties of solutions to a nonlinear system describing the motion of a bar in which the middle part is sensitive to the thermal change, while the outer parts are insensible. By the energy method, we show that the initial boundary value problem for this coupled system of wave equations and thermoelastic equations with second sound in one space variable is well-posed globally in time, and it is also stable exponentially as the time goes to infinity when the wave speed of the outer parts is properly large, under certain restrictions on the initial data and the growth rate of the nonlinear terms.

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.

Exponential stability for nonlinear thermoelastic equations with second sound

2010 ◽  
Vol 11 (4) ◽  
pp. 2502-2513 ◽  
Author(s):  
Yuming Qin ◽  
Zhiyong Ma ◽  
Xinguang Yang
Keyword(s):  
Exponential Stability ◽  
Second Sound
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