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

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 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.

scholarly journals EXPONENTIAL DECAY OF THERMO-ELASTIC BRESSE SYSTEM WITH DISTRIBUTED DELAY TERM

2017 ◽  
Vol 47 (6) ◽  
Author(s):  
Salah Zitouni ◽  
Lamine Bouzettouta ◽  
Khaled Zennir ◽  
Djamel Ouchenane
Keyword(s):  
Exponential Decay ◽  
Distributed Delay ◽  
Delay Term ◽  
Bresse System

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 Cross immunity protection and antibody dependent enhancement: A distributed delay dynamic model

2021 ◽  
Author(s):  
Vanessa Steindorf ◽  
Sergio Oliva
Keyword(s):  
Dengue Fever ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Distributed Delay ◽  
Global Dynamics ◽  
Antibody Dependent Enhancement ◽  
Delay Term ◽  
Cross Immunity ◽  
Steady Solutions ◽  
Bifurcation Structures

Dengue fever is endemic in tropical and sub-tropical countries, and some of the important features of Dengue fever spread continues to pose challenges for mathematical modelling. Here, we propose a system of integro-differential equations (IDE) to study the disease transmission dynamics that involves multiserotypes and cross immunity. Our main objective is to incorporate and analyze the effect of a general time delay term describing acquired cross immunity protection and the effect of antibody dependent enhancement (ADE), both characteristics of Dengue fever. We perform qualitative analysis of the model and obtain results to show the stability of the epidemiologically important steady solutions that is completely determined by the basic reproduction number and the invasion reproduction number. We establish the global dynamics, by constructing suitable Lyapunov functions. We also conduct some numerical experiments to illustrate bifurcation structures, indicating the occurrence of periodic oscillations for specific range of values of a key parameter representing the ADE.

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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