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 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 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.

Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

2021 ◽  
pp. 2150219
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Distributed Delay ◽  
Real Data ◽  
Least Square ◽  
Order Model ◽  
The Real ◽  
Fractional Order Model ◽  
Different Types ◽  
Distributed Time Delay

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo–Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo–Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo–Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

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