scholarly journals GLOBAL EXISTENCE OF TIMOSHENKO SYSTEM WITH RESPECT TO FRACTIONAL MEMORY OPERATOR, SPATIAL FRACTIONAL THERMAL EFFECT AND DISTRIBUTED DELAY

Fractals ◽  
2021 ◽  
pp. 2240006
Author(s):  
ABDELBAKI CHOUCHA ◽  
SALAH BOULAARAS ◽  
DJAMEL OUCHENANE ◽  
ASMA ALHARBI ◽  
MOHAMED ABDALLA
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Thermal Effect ◽  
Distributed Delay ◽  
Fractional Operator ◽  
Timoshenko System ◽  
Delay Term ◽  
Semigroup Method ◽  
The Stability

In this paper, the Timoshenko system with distributed delay term, fractional operator in the memory and spatial fractional thermal effect is considered, we will prove under some assumptions the global existence of a weak solution. Furthermore, we show some results about the stability of system by the semigroup method.

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 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 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.

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

scholarly journals The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wen-Juan Wang ◽  
Yan Jia
Keyword(s):  
Weak Solution ◽  
Asymptotic Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Perturbed System ◽  
Regular Class ◽  
Stability Issue ◽  
The Stability

We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solutionuof the Navier-Stokes equations lies in the regular class∇u∈Lp(0,∞;Bq,∞0(ℝ3)),(2α/p)+(3/q)=2α,2<q<∞,0<α<1, then every weak solutionv(x,t)of the perturbed system converges asymptotically tou(x,t)asvt-utL2→0,t→∞.

scholarly journals Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Fatmawati ◽  
Muhammad Altaf Khan ◽  
Cicik Alfiniyah ◽  
Ebraheem Alzahrani
Keyword(s):  
Statistical Data ◽  
Dengue Infection ◽  
Fractional Operator ◽  
Novel Approach ◽  
Reduction Number ◽  
Best Fitting ◽  
The Stability ◽  
Parameter Values ◽  
Graphical Illustration ◽  
Stability Results

AbstractIn this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ R 0 ≈ 2.2020 . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ R 0 < 1 . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.

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