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.

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 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.

Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound

2019 ◽  
Vol 26 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Convex Functions ◽  
Semigroup Theory ◽  
General Decay ◽  
Well Posedness ◽  
Second Sound ◽  
Nonlinear Feedback ◽  
Damping Term ◽  
General Decay Rate ◽  
One Dimensional

Abstract In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term.

scholarly journals Asymptotic stability of porous-elastic system with thermoelasticity of type III

2021 ◽  
Author(s):  
Ilyes Lacheheb ◽  
Salim A. Messaoudi ◽  
Mostafa Zahri
Keyword(s):  
Wave Propagation ◽  
Asymptotic Stability ◽  
Finite Difference ◽  
Elastic System ◽  
Well Posedness ◽  
One Dimensional ◽  
Type Iii ◽  
The Stability ◽  
Theoretical Results ◽  
Finite Difference Techniques

AbstractIn this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. At the end, we use some numerical approximations based on finite difference techniques to validate the theoretical results.

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.

Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling

1964 ◽  
Vol 31 (3) ◽  
pp. 423-429 ◽  
Author(s):  
Robert C. Petrof ◽  
Serge Gratch
Keyword(s):  
Wave Propagation ◽  
Elastic System ◽  
Thermomechanical Coupling ◽  
Temperature Dependent ◽  
Stress Variation ◽  
Single Degree Of Freedom ◽  
One Dimensional ◽  
Stress Strain Relation ◽  
Longitudinal Wave Propagation ◽  
Temperature Dependent Properties

A numerical method is developed for the analysis of one-dimensional wave propagation in viscoelastic media with temperature-dependent properties when thermomechanical coupling is significant. The method is applied to a specific case of longitudinal wave propagation in a finite rod with essentially sinusoidal stress variation at the two ends. The results show that, contrary to the usual assumption, such a system does not have the same response as a single-degree-of-freedom elastic system with viscous damping, as long as a realistic stress-strain relation is used.

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 Energy decay for a degeneratewave equation under fractional derivative controls

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6045-6072
Author(s):  
Abbes Benaissa ◽  
Chahira Aichi
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Boundary Control ◽  
Semigroup Theory ◽  
Energy Decay ◽  
Linear Operators ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Spectrum Method ◽  
Derivative Type

In this article, we consider a one-dimensional degenerate wave equation with a boundary control condition of fractional derivative type. We show that the problem is not uniformly stable by a spectrum method and we study the polynomial stability using the semigroup theory of linear operators.

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