scholarly journals A uniform stability result for thermoelasticity of type III with boundary distributed delay

2014 ◽  
Vol 415 (1) ◽  
pp. 148-158 ◽  
Author(s):  
Muhammad I. Mustafa
Keyword(s):  
Distributed Delay ◽  
Stability Result ◽  
Uniform Stability ◽  
Type Iii

scholarly journals On the System of Coupled Nondegenerate Kirchhoff Equations with Distributed Delay: Global Existence and Exponential Decay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Salem Alkhalaf ◽  
Ibrahim Mekawy ◽  
...  
Keyword(s):  
Global Existence ◽  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Energy Method ◽  
Existence Of Solutions ◽  
Distributed Delay ◽  
Stability Result ◽  
Kirchhoff Equations ◽  
Global Existence Of Solutions

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

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 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.

scholarly journals Stability Result for a Weakly Nonlinearly Damped Porous System with Distributed Delay

2021 ◽  
Vol 19 (6) ◽  
pp. 812-825
Author(s):  
Khoudir Kibeche ◽  
Lamine Bouzettouta ◽  
Abdelhak Djebabla ◽  
Fahima Hebhoub
Keyword(s):  
Distributed Delay ◽  
Stability Result ◽  
Porous System ◽  
Nonlinear Feedback ◽  
Damping Term ◽  
General Decay Rate ◽  
Weakly Nonlinear ◽  
Delay Term ◽  
Research Areas ◽  
Speed Of Propagation

In this paper, we consider a one-dimensional porous system damped with a single weakly nonlinear feedback and distributed delay term. Without imposing any restrictive growth assumption near the origin on the damping term, we establish an explicit and general decay rate, using a multiplier method and some properties of convex functions in case of the same speed of propagation in the two equations of the system. The result is new and opens more research areas into porous-elastic system.

A stability result for the vibrations given by the standard linear model with thermoelasticity of type III

2017 ◽  
Vol 97 (10) ◽  
pp. 1688-1700 ◽  
Author(s):  
Tijani A. Apalara ◽  
Salim A. Messaoudi ◽  
Jamal H. Al-Smail
Keyword(s):  
Linear Model ◽  
Stability Result ◽  
Type Iii ◽  
Standard Linear

scholarly journals Polynomial stability of the wave equation with distributed delay term on the dynamical control

2021 ◽  
Vol 8 (1) ◽  
pp. 207-227
Author(s):  
Roland Silga ◽  
Gilbert Bayili
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Distributed Delay ◽  
Strong Stability ◽  
Uniform Stability ◽  
Polynomial Stability ◽  
Delay Term ◽  
Dynamical Control ◽  
Frequency Domain Approach

Abstract Using the frequency domain approach, we prove the rational stability for a wave equation with distributed delay on the dynamical control, after establishing the strong stability and the lack of uniform stability.

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