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.

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 New stability result for a Bresse system with one infinite memory in the shear angle equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Saeed M. Ali
Keyword(s):  
Asymptotic Stability ◽  
Initial Data ◽  
General Condition ◽  
Relaxation Function ◽  
Stability Result ◽  
Shear Angle ◽  
Boundedness Condition ◽  
Infinite Memory ◽  
One Dimensional ◽  
Bresse System

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory acting in the second equation (the shear angle equation) of the system. We prove that the asymptotic stability of the system holds under some general condition imposed into the relaxation function, precisely,</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ g^{\prime}(t)\le -\xi(t) G(g(t)). $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data <inline-formula><tex-math id="M1">\begin{document}$ \eta{0x} $\end{document}</tex-math></inline-formula>. This study generalizes and improves previous literature outcomes.</p>

scholarly journals Uniform and weak stability of Bresse system with one infinite memory in the shear angle displacements

2021 ◽  
Author(s):  
Rania Bekhouche ◽  
Aissa Guesmia ◽  
Salim Messaoudi
Keyword(s):  
Semigroup Theory ◽  
Open Interval ◽  
Weak Decay ◽  
Shear Angle ◽  
Well Posedness ◽  
Decay Estimates ◽  
Weak Stability ◽  
Infinite Memory ◽  
One Dimensional ◽  
Bresse System

AbstractIn this paper, we consider a one-dimensional linear Bresse system in a bounded open interval with one infinite memory acting only on the shear angle equation. First, we establish the well posedness using the semigroup theory. Then, we prove two general (uniform and weak) decay estimates depending on the speeds of wave propagations and the arbitrary growth at infinity of the relaxation function.

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 Well-posedness and energy decay of swelling porous elastic soils with a second sound and delay term

2021 ◽  
Author(s):  
Abdelli Manel ◽  
Lamine Bouzettouta ◽  
Guesmia Amar ◽  
Baibeche Sabah
Keyword(s):  
Wave Propagation ◽  
Delay Time ◽  
Elastic System ◽  
Semigroup Theory ◽  
Energy Decay ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term

In this paper we consider a one-dimensional swelling porous-elastic system with second sound and delay term acting on the porous equation. Under suitable assumptions on the weight of delay, we establish the well-posedness of the system by using semigroup theory and we prove that the unique dissipation due to the delay time is strong enough to exponentially stabilize the system when the speeds of wave propagation are equal.

scholarly journals On the Porous-Elastic System with Thermoelasticity of Type III and Distributed Delay: Well-Posedness and Stability

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Djamel Ouchenane ◽  
Abdelbaki Choucha ◽  
Mohamed Abdalla ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif
Keyword(s):  
Lyapunov Functions ◽  
Elastic System ◽  
Distributed Delay ◽  
Mathematical Physics ◽  
Well Posedness ◽  
Engineering Structures ◽  
One Dimensional ◽  
Delay Term ◽  
Type Iii ◽  
The Stability

The paper deals with a one-dimensional porous-elastic system with thermoelasticity of type III and distributed delay term. This model is dealing with dynamics of engineering structures and nonclassical problems of mathematical physics. We establish the well posedness of the system, and by the energy method combined with Lyapunov functions, we discuss the stability of system for both cases of equal and nonequal speeds of wave propagation.

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.

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