scholarly journals Global Existence for Two Singular One-Dimensional Nonlinear Viscoelastic Equations with respect to Distributed Delay Term

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Ali Allahem
Keyword(s):  
Global Existence ◽  
Global Solution ◽  
Energy Method ◽  
Distributed Delay ◽  
Potential Well ◽  
One Dimensional ◽  
Delay Term ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equations ◽  
General Source

In this current work, we are interested in a system of two singular one-dimensional nonlinear equations with a viscoelastic, general source and distributed delay terms. The existence of a global solution is established by the theory of potential well, and by using the energy method with the function of Lyapunov, we prove the general decay result of our system.

scholarly journals Global Existence and Decay for a System of Two Singular Nonlinear Viscoelastic Equations with General Source and Localized Frictional Damping Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Nadia Mezouar ◽  
Ahmad Mohammed Alghamdi
Keyword(s):  
Boundary Condition ◽  
Lyapunov Functional ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Dimensional System ◽  
One Dimensional ◽  
Nonlinear Viscoelastic ◽  
Frictional Damping ◽  
Viscoelastic Equations ◽  
General Source

The current paper deals with the proof of a global solution of a viscoelasticity singular one-dimensional system with localized frictional damping and general source terms, taking into consideration nonlocal boundary condition. Moreover, similar to that in Boulaaras’ recent studies by constructing a Lyapunov functional and use it together with the perturbed energy method in order to prove a general decay result.

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 Global existence and asymptotic behavior for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, distributed delay and Balakrishnan-Taylor damping terms

2021 ◽  
Vol 7 (3) ◽  
pp. 4517-4539
Author(s):  
Abdelbaki Choucha ◽  
◽  
Salah Boulaaras ◽  
Asma Alharbi ◽  
◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

<abstract><p>A nonlinear viscoelastic Kirchhoff-type equation with a logarithmic nonlinearity, Balakrishnan-Taylor damping, dispersion and distributed delay terms is studied. We establish the global existence of the solutions of the problem and by the energy method we prove an explicit and general decay rate result under suitable hypothesis.</p></abstract>

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 Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

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 Global Existence and Decay of Solutions for Coupled Nondegenerate Kirchhoff System with a Time Varying Delay Term

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Nadia Mezouar ◽  
Salah Mahmoud Boulaaras ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Global Existence ◽  
Stability Estimate ◽  
Time Varying ◽  
Delay Term ◽  
Time Varying Delay ◽  
Global Existence Of Solutions ◽  
Nonlinear Viscoelastic ◽  
Decay Of Solutions ◽  
Weight Condition ◽  
Varying Delay

This paper deals with the global existence of solutions in a bounded domain for nonlinear viscoelastic Kirchhoff system with a time varying delay by using the energy and Faedo–Galerkin method with respect to the delay term weight condition in the feedback and the delay speed. Furthermore, by using some convex functions properties, we prove a uniform stability estimate.

Global Existence for Two Laser Models

1997 ◽  
Vol 07 (03) ◽  
pp. 363-384
Author(s):  
B. Ducomet
Keyword(s):  
Global Existence ◽  
Laser Physics ◽  
Global Solution ◽  
Global Attractor ◽  
One Dimensional ◽  
Dimensional Models ◽  
Nonlinear Regimes

We compare two one-dimensional models giving a simplified description for some nonlinear regimes in laser physics. For these two models, we prove the existence of a global solution, and, for one of them, the existence of a global attractor.

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