scholarly journals Exponential Stability of Swelling Porous Elastic with a Viscoelastic Damping and Distributed Delay Term

2021 ◽  
Vol 2021 ◽  
pp. 1-8 ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Bahri Belkacem Cherif ◽  
Mohamed Abdalla
Keyword(s):  
Exponential Stability ◽  
Elastic System ◽  
Distributed Delay ◽  
General Decay ◽  
Multiplier Method ◽  
Viscoelastic Damping ◽  
Asymptotic Behaviors ◽  
Delay Term

In this paper, we consider a swelling porous elastic system with a viscoelastic damping and distributed delay terms in the second equation. The coupling gives new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils. The general decay result is established by the multiplier method.

scholarly journals General Decay of Solutions in One-Dimensional Porous-Elastic with Memory and Distributed Delay Term

2021 ◽  
Vol 52 ◽  
Author(s):  
Abdelbaki Choucha ◽  
Djamel Ouchenane ◽  
Khaled Zennir
Keyword(s):  
Energy Method ◽  
Elastic System ◽  
Distributed Delay ◽  
General Decay ◽  
Lyapunov Functionals ◽  
One Dimensional ◽  
Delay Term ◽  
Decay Of Solutions ◽  
With Memory

As a continuity to the study by T. A. Apalarain[3], we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result given in Theorem 2.1.

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.

General decay of porous elastic system with thermo-viscoelastic damping

2021 ◽  
Vol 9 (1) ◽  
pp. 31-43
Author(s):  
F. Djellali ◽  
◽  
S. Labidi ◽  
F. Taallah ◽  
◽  
...  
Keyword(s):  
Heat Flux ◽  
Elastic System ◽  
General Decay ◽  
Viscoelastic Damping ◽  
Stability Number ◽  
Memory Kernel ◽  
One Dimensional

In this work, we consider a one-dimensional porous thermoelastic system, where the heat flux used is introduced by Green and Naghdi theories. We establish a general decay result depending on the memory kernel and a new introduced stability number.

scholarly journals Exponential Stabilization of a Swelling Porous-Elastic System with Microtemperature Effect and Distributed Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Bahri Belkacem Cherif ◽  
Muajebah Hidan ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Elastic System ◽  
Distributed Delay ◽  
Stability Result ◽  
Exponential Stabilization ◽  
Well Posedness

The swelling porous thermoelastic system with the presence of temperatures, microtemperature effect, and distributed delay terms is considered. We will establish the well posedness of the system, and we prove the exponential stability result.

Explicit Stability for a Porous Thermoelastic System with Second Sound and Distributed Delay Term

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Abdelhak Djebabla ◽  
Abdelbaki Choucha ◽  
Djamel Ouchenane ◽  
Khaled Zennir
Keyword(s):  
Distributed Delay ◽  
Second Sound ◽  
Delay Term

scholarly journals A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
M. Iswarya ◽  
R. Raja ◽  
G. Rajchakit ◽  
J. Cao ◽  
J. Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Lyapunov Functional ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Theoretic Approach ◽  
Discrete Time Delay

AbstractIn this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

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