Polynomial Stability for Timoshenko-Type System with Past History

2014 ◽  
Vol 623 ◽  
pp. 78-84
Author(s):  
Zhi Yong Ma
Keyword(s):  
Relaxation Function ◽  
Wave Speed ◽  
Past History ◽  
Type System ◽  
Stability Result ◽  
Equation Modeling ◽  
Polynomial Stability ◽  
Timoshenko Type ◽  
Semigroup Method ◽  
Vibrating Systems

In this paper, we consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. We use semigroup method to prove the polynomial stability result with assumptions on past history relaxation function exponentially decaying for the nonequal wave-speed case.

scholarly journals Uniform decay in a Timoshenko-type system with past history

2009 ◽  
Vol 360 (2) ◽  
pp. 459-475 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Belkacem Said-Houari
Keyword(s):  
Past History ◽  
Type System ◽  
Uniform Decay ◽  
Timoshenko Type

scholarly journals On the Stability of a Laminated Beam With Structural Damping and Gurtin-Pipkin Thermal Law

2018 ◽  
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Exponential Stability ◽  
Relaxation Function ◽  
Equation Modeling ◽  
Well Posedness ◽  
Structural Damping ◽  
Laminated Beam ◽  
One Dimensional ◽  
Semigroup Method ◽  
Lack Of Exponential Stability ◽  
The Stability

In this paper, we investigate the stabilization of a one-dimensional thermoelastic laminated beam with structural damping, coupled to a heat equation modeling an expectedly dissipative effect through heat conduction governed by Gurtin-Pipkin thermal law. Under some assumptions on the relaxation function g, we establish the well-posedness for the problem. Furthermore, we prove the exponential stability and lack of exponential stability for the problem. To achieve our goals, we make use of the semigroup method, the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem.

Asymptotic behavior of the Timoshenko-type system with nonlinear boundary control

2019 ◽  
Vol 10 (2) ◽  
pp. 171-182
Author(s):  
Mohamed Ali Ayadi ◽  
Ahmed Bchatnia
Keyword(s):  
Asymptotic Behavior ◽  
Wide Class ◽  
Existence And Uniqueness ◽  
Relaxation Function ◽  
Nonlinear Boundary ◽  
Type System ◽  
Timoshenko Type ◽  
Uniqueness Of The Solution ◽  
Boundary Dissipation ◽  
Nonlinear Boundary Control

AbstractIn this paper, we consider the Timoshenko-type system with nonlinear boundary dissipation. We prove the existence and uniqueness of the solution and we establish an explicit and general decay result for a wide class of the relaxation function, which depends on the length of the beam.

scholarly journals Well-Posedness and Asymptotic Stability to a Laminated Beam in Thermoelasticity of Type III

2018 ◽  
Author(s):  
Yue Luan ◽  
Wenjun Liu ◽  
Gang Li
Keyword(s):  
Asymptotic Stability ◽  
Stability Result ◽  
Well Posedness ◽  
Polynomial Stability ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Type Iii ◽  
Semigroup Method ◽  
Exponentially Stable ◽  
Lack Of Exponential Stability

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first give the well-posedness of the system by using the semigroup method. Then, we show that the system is exponentially stable under the assumption of equal wave speeds. Furthermore, it is proved that the system is lack of exponential stability for case of nonequal wave speeds. In this regard, a polynomial stability result is proved.

scholarly journals A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Djamel Ouchenane ◽  
Zineb Khalili ◽  
Fares Yazid ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Past History ◽  
Stability Result ◽  
Shear Angle ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term ◽  
Bresse System ◽  
Semigroup Method

We consider a one-dimensional linear thermoelastic Bresse system with delay term, forcing, and infinity history acting on the shear angle displacement. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability result of global solution is obtained.

scholarly journals Exponential stability for a Timoshenko-type system with history

2011 ◽  
Vol 380 (1) ◽  
pp. 299-312 ◽  
Author(s):  
Zhiyong Ma ◽  
Lingrui Zhang ◽  
Xinguang Yang
Keyword(s):  
Exponential Stability ◽  
Type System ◽  
Timoshenko Type
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