Well-posedness and stability for a Moore-Gibson-Thompson equation with internal distributed delay

2021 ◽  
Vol 10 (4) ◽  
pp. 693-703
Author(s):  
Abdelkader Braik ◽  
Abderrahmane Beniani ◽  
Khaled Zennir
Keyword(s):  
Distributed Delay ◽  
Well Posedness

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 Well-posedness and asymptotic stability for the Lamé system with internal distributed delay

2018 ◽  
Vol 22 (1) ◽  
pp. 31-41 ◽  
Author(s):  
Noureddine Taouaf ◽  
Noureddine Amroun ◽  
Abbes Benaissa ◽  
Abderrahmane Beniani
Keyword(s):  
Asymptotic Stability ◽  
Distributed Delay ◽  
Well Posedness ◽  
Lamé System ◽  
Lame System

scholarly journals Analysis of a Predator-Prey Model with Distributed Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Gunasundari Chandrasekar ◽  
Salah Mahmoud Boulaaras ◽  
Senthilkumaran Murugaiah ◽  
Arul Joseph Gnanaprakasam ◽  
Bahri Belkacem Cherif
Keyword(s):  
Distributed Delay ◽  
Nonequilibrium Dynamics ◽  
Global Dynamics ◽  
Well Posedness ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Mean Delay ◽  
Prey Model ◽  
Local And Global Dynamics ◽  
The Mean

In this paper, we consider a predator-prey model, where we assumed that the model to be an infected predator-free equilibrium one. The model includes a distributed delay to describe the time between the predator’s capture of the prey and its conversion to biomass for predators. When the delay is absent, the model exhibits asymptotic convergence to an equilibrium. Therefore, any nonequilibrium dynamics in the model when the delay is included can be attributed to the delay’s inclusion. We assume that the delay is distributed and model the delay using integrodifferential equations. We established the well-posedness and basic properties of solutions of the model with nonspecified delay. Then, we analyzed the local and global dynamics as the mean delay varies.

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.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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