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 Uniform stability for a type III thermoelastic laminated beam with structural damping

2022 ◽  
Author(s):  
Fayssal Djellali
Keyword(s):  
Heat Flux ◽  
Exponential Stability ◽  
Semigroup Theory ◽  
Stability Result ◽  
Uniform Stability ◽  
Well Posedness ◽  
Structural Damping ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Lack Of Exponential Stability

In this work, we consider a thermoelastic laminated beam with structural damping, where the heat flux is given by Green and Naghdi theories. We establish the well-posedness of the system using semigroup theory. Moreover, under the condition of equal wave speeds, we prove an exponential stability result for the considered system. In the case of lack of exponential stability we show that the solution decays polynomially.

scholarly journals Well-posedness and exponential decay for a laminated beam in thermoelasticity of type III with delay term

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 58-76
Author(s):  
Douib Madani ◽  
Salah Zitouni ◽  
Djebabla Abdelhak
Keyword(s):  
Asymptotic Behaviour ◽  
Exponential Decay ◽  
Well Posedness ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Delay Term ◽  
Type Iii ◽  
Asymptotic Behaviour Of Solutions ◽  
Exponentially Stable ◽  
Well Posed

We study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the first equation. We show that the system is well-posed by using Lumer-Philips theorem and prove that the system is exponentially stable if and only if the wave speeds are equal.

A stability result of a Timoshenko system in thermoelasticity of second sound with a delay term in the internal feedback

2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Djamel Ouchenane
Keyword(s):  
Heat Conduction ◽  
Stability Result ◽  
Well Posedness ◽  
Second Sound ◽  
Timoshenko System ◽  
Wave Speeds ◽  
One Dimensional ◽  
Delay Term ◽  
Semigroup Method ◽  
Cattaneo’S Law

AbstractIn this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay term in the feedback. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem. Furthermore, an exponential stability result is shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.

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.

Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III

2019 ◽  
Vol 43 (6) ◽  
pp. 3148-3166 ◽  
Author(s):  
Wenjun Liu ◽  
Yue Luan ◽  
Yadong Liu ◽  
Gang Li
Keyword(s):  
Asymptotic Stability ◽  
Well Posedness ◽  
Laminated Beam ◽  
Type Iii

scholarly journals Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

2017 ◽  
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Heat Conduction ◽  
Rotation Angle ◽  
Polynomial Decay ◽  
Well Posedness ◽  
Laminated Beam ◽  
Wave Speeds ◽  
One Dimensional ◽  
Beam System ◽  
Exponentially Stable ◽  
Well Posed

In this paper, we study the well-posedness and the asymptotic behavior of a one-dimensional laminated beam system, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using the Hille-Yosida theorem and prove that the system is exponentially stable if and only if the wave speeds are equal. Furthermore, we show that the system is polynomially stable provided that the wave speeds are not equal.

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.

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 On the stability of a laminated beam with structural damping and Gurt–Pipkin thermal law

2021 ◽  
Vol 26 (3) ◽  
pp. 396-418
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Exponential Stability ◽  
Relaxation Function ◽  
Equation Modeling ◽  
Well Posedness ◽  
Structural Damping ◽  
Stability Number ◽  
Laminated Beam ◽  
One Dimensional ◽  
Lack Of Exponential Stability ◽  
The Stability

In this paper, we investigate the stabilization of a one-dimensional thermoelastic laminated beam with structural damping coupled with 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 of the problem by using Lumer–Phillips theorem. Furthermore, we prove the exponential stability and lack of exponential stability depending on a stability number by using the perturbed energy method and Gearhart–Herbst–Prüss–Huang theorem, respectively.

scholarly journals Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

2019 ◽  
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Heat Conduction ◽  
Energy Method ◽  
Rotation Angle ◽  
Polynomial Decay ◽  
Structural Damping ◽  
Laminated Beam ◽  
Wave Speeds ◽  
One Dimensional ◽  
Exponentially Stable ◽  
Well Posed

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

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