Well-posedness and stability of nonautonomous past systems with unbounded operators in the delay term

2021 ◽  
Author(s):  
Samir Boujijane ◽  
Said Boulite ◽  
Lahcen Maniar
Keyword(s):  
Well Posedness ◽  
Unbounded Operators ◽  
Delay Term

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 Global Well-Posedness and Stability for a Viscoelastic Plate Equation with a Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Baowei Feng
Keyword(s):  
Time Delay ◽  
Boundary Value Problem ◽  
Viscoelastic Plate ◽  
Energy Estimates ◽  
Memory Term ◽  
Well Posedness ◽  
Plate Equation ◽  
Delay Term ◽  
Galerkin Approximations ◽  
Energy Perturbation

A plate equation with a memory term and a time delay term in the internal feedback is investigated. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates. Moreover, by using energy perturbation method, we prove a general decay result of the energy provided that the weight of the delay is less than the weight of the damping.

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 exponential decay for a laminated beam in thermoelasticity of type III with delay term

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 58-76
Author(s):  
Douib Madani ◽  
Salah Zitouni ◽  
Djebabla Abdelhak
Keyword(s):  
Asymptotic Behaviour ◽  
Exponential Decay ◽  
Well Posedness ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Delay Term ◽  
Type Iii ◽  
Asymptotic Behaviour Of Solutions ◽  
Exponentially Stable ◽  
Well Posed

We study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the first equation. We show that the system is well-posed by using Lumer-Philips theorem and prove that the system is exponentially stable if and only if the wave speeds are equal.

scholarly journals Well-Posedness and Asymptotic Stability of Solutions to the Bresse System under Cattaneo's Law with Infinite Memories and Time-Varying Delays

2017 ◽  
Author(s):  
Gang Li ◽  
Xiangyu Kong
Keyword(s):  
Time Dependent ◽  
Lyapunov Functionals ◽  
Well Posedness ◽  
Time Varying ◽  
Stability Of Solutions ◽  
One Dimensional ◽  
Delay Term ◽  
Relaxation Functions ◽  
Well Posed ◽  
Cattaneo’S Law

In this paper, we study a one-dimensional Bresse-Cattaneo system with infinite memories and time-dependent delay term (the coefficient of which is not necessarily positive) in the internal feedbacks. First, it is proved that the system is well-posed by means of the Hille-Yosida theorem under suitable assumptions on the relaxation functions. Then, without any restriction on the speeds of wave propagations, we establish the exponential or general decay result by introducing suitable energy and Lyapunov functionals.

Sign in / Sign up

Export Citation Format

Share Document