Exponential decay of solutions for a viscoelastic coupled Lame system with logarithmic source and distributed delay terms

2020 ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras ◽  
Djamel Ouchenane
Keyword(s):  
Exponential Decay ◽  
Distributed Delay ◽  
Lamé System ◽  
Decay Of Solutions ◽  
Lame System

scholarly journals Polynomial Decay Rate for a Coupled Lamé System with Viscoelastic Damping and Distributed Delay Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Nadjat Doudi ◽  
Salah Mahmoud Boulaaras ◽  
Ahmad Mohammed Alghamdi ◽  
Bahri Cherif
Keyword(s):  
Lyapunov Functional ◽  
Distributed Delay ◽  
Energy Decay ◽  
Polynomial Decay ◽  
Viscoelastic Damping ◽  
Lamé System ◽  
Relaxation Functions ◽  
General Energy ◽  
Lame System ◽  
Distributed Time Delay

In this paper, we prove a general energy decay results of a coupled Lamé system with distributed time delay. By assuming a more general of relaxation functions and using some properties of convex functions, we establish the general energy decay results to the system by using an appropriate Lyapunov functional.

scholarly journals Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Salah Boulaaras ◽  
Nadjat Doudi
Keyword(s):  
Global Existence ◽  
Lyapunov Functional ◽  
Source Term ◽  
Distributed Delay ◽  
Memory Term ◽  
Lamé System ◽  
Relaxation Functions ◽  
Exponential Energy Decay ◽  
Lame System ◽  
Distributed Time Delay

AbstractIn this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation functions, and some properties of convex functions are considered.

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 Well-posedness and exponential stability for coupled Lamé system with a viscoelastic damping

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3591-3598
Author(s):  
Noureddine Taouaf ◽  
Noureddine Amroun ◽  
Abbes Benaissa ◽  
Abderrahmane Beniani
Keyword(s):  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Viscoelastic Damping ◽  
Well Posedness ◽  
Lamé System ◽  
Lame System

In this paper, we consider a coupled Lam? system with a viscoelastic damping in the first equation. We prove well-posedness by using Faedo-Galerkin method and establish an exponential decay result by introducing a suitable Lyaponov functional.

scholarly journals Exponential Decay for a System of Equations with Distributed Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Nasser-Eddine Tatar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Exponential Decay ◽  
Distributed Delay ◽  
Distributed Delays ◽  
System Of Equations ◽  
Activation Functions ◽  
Convergence Of Solutions

We prove convergence of solutions to zero in an exponential manner for a system of ordinary differential equations. The feature of this work is that it deals with nonlinear non-Lipschitz and unbounded distributed delay terms involving non-Lipschitz and unbounded activation functions.

scholarly journals The first mixed problem for the nonstationary Lamé system

2017 ◽  
Vol 47 (8) ◽  
pp. 2731-2756 ◽  
Author(s):  
O.I. Makhmudov ◽  
N. Tarkhanov
Keyword(s):  
Mixed Problem ◽  
Lamé System ◽  
Lame System

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.

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