scholarly journals Uniform and weak stability of Bresse system with one infinite memory in the shear angle displacements

2021 ◽  
Author(s):  
Rania Bekhouche ◽  
Aissa Guesmia ◽  
Salim Messaoudi
Keyword(s):  
Semigroup Theory ◽  
Open Interval ◽  
Weak Decay ◽  
Shear Angle ◽  
Well Posedness ◽  
Decay Estimates ◽  
Weak Stability ◽  
Infinite Memory ◽  
One Dimensional ◽  
Bresse System

AbstractIn this paper, we consider a one-dimensional linear Bresse system in a bounded open interval with one infinite memory acting only on the shear angle equation. First, we establish the well posedness using the semigroup theory. Then, we prove two general (uniform and weak) decay estimates depending on the speeds of wave propagations and the arbitrary growth at infinity of the relaxation function.

scholarly journals New stability result for a Bresse system with one infinite memory in the shear angle equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Saeed M. Ali
Keyword(s):  
Asymptotic Stability ◽  
Initial Data ◽  
General Condition ◽  
Relaxation Function ◽  
Stability Result ◽  
Shear Angle ◽  
Boundedness Condition ◽  
Infinite Memory ◽  
One Dimensional ◽  
Bresse System

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory acting in the second equation (the shear angle equation) of the system. We prove that the asymptotic stability of the system holds under some general condition imposed into the relaxation function, precisely,</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ g^{\prime}(t)\le -\xi(t) G(g(t)). $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data <inline-formula><tex-math id="M1">\begin{document}$ \eta{0x} $\end{document}</tex-math></inline-formula>. This study generalizes and improves previous literature outcomes.</p>

scholarly journals A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Djamel Ouchenane ◽  
Zineb Khalili ◽  
Fares Yazid ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Past History ◽  
Stability Result ◽  
Shear Angle ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term ◽  
Bresse System ◽  
Semigroup Method

We consider a one-dimensional linear thermoelastic Bresse system with delay term, forcing, and infinity history acting on the shear angle displacement. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability result of global solution is obtained.

Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound

2019 ◽  
Vol 26 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Convex Functions ◽  
Semigroup Theory ◽  
General Decay ◽  
Well Posedness ◽  
Second Sound ◽  
Nonlinear Feedback ◽  
Damping Term ◽  
General Decay Rate ◽  
One Dimensional

Abstract In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term.

scholarly journals Well-posedness and energy decay of swelling porous elastic soils with a second sound and delay term

2021 ◽  
Author(s):  
Abdelli Manel ◽  
Lamine Bouzettouta ◽  
Guesmia Amar ◽  
Baibeche Sabah
Keyword(s):  
Wave Propagation ◽  
Delay Time ◽  
Elastic System ◽  
Semigroup Theory ◽  
Energy Decay ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term

In this paper we consider a one-dimensional swelling porous-elastic system with second sound and delay term acting on the porous equation. Under suitable assumptions on the weight of delay, we establish the well-posedness of the system by using semigroup theory and we prove that the unique dissipation due to the delay time is strong enough to exponentially stabilize the system when the speeds of wave propagation are equal.

Well-Posedness of the Gnedenko System with Multiple Vacations

2012 ◽  
Vol 522 ◽  
pp. 902-909
Author(s):  
Bilikiz Yunus ◽  
Abdukerim Haji
Keyword(s):  
Semigroup Theory ◽  
Linear Operators ◽  
Well Posedness ◽  
Multiple Vacations ◽  
Dynamic Solution ◽  
Multiple Vacation ◽  
Gnedenko System

We investigate the solution of the Gnedenko system with multiple vacation of a repairman. By using-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

Error feedback regulation for 1D anti-stable wave equation

2021 ◽  
pp. 014233122110592
Author(s):  
Zhiyuan Li ◽  
Feng-Fei Jin
Keyword(s):  
Wave Equation ◽  
Tracking Error ◽  
Feedback Regulation ◽  
Original System ◽  
Well Posedness ◽  
Error Feedback ◽  
One Dimensional ◽  
Internal Loop ◽  
Finite Dimensional ◽  
Uniformly Bounded

This paper is concerned with the boundary error feedback regulation for a one-dimensional anti-stable wave equation with distributed disturbance generated by a finite-dimensional exogenous system. Transport equation and regulator equation are introduced first to deal with the anti-damping on boundary and the distributed disturbance of the original system. Then, the tracking error and its derivative are measured to design an observer for both exosystem and auxiliary partial differential equation (PDE) system to recover the state. After proving the well-posedness of the regulator equations, we propose an observer-based controller to regulate the tracking error to zero exponentially and keep the states of all the internal loop uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed controller.

scholarly journals Hyperbolic Maxwell variational inequalities of the second kind

2020 ◽  
Vol 26 ◽  
pp. 34 ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Variational Inequalities ◽  
Existence Result ◽  
Semigroup Theory ◽  
Regularity Property ◽  
Well Posedness ◽  
Test Functions ◽  
Local Boundedness ◽  
Subdifferential Calculus ◽  
Faraday’S Law ◽  
Yosida Regularization

We analyze a class of hyperbolic Maxwell variational inequalities of the second kind. By means of a local boundedness assumption on the subdifferential of the underlying nonlinearity, we prove a well-posedness result, where the main tools for the proof are the semigroup theory for Maxwell’s equations, the Yosida regularization and the subdifferential calculus. The second part of the paper focuses on a more general case omitting the local boundedness assumption. In this case, taking into account more regular initial data and test functions, we are able to prove a weaker existence result through the use of the minimal section operator associated with the Nemytskii operator of the governing subdifferential. Eventually, we transfer the developed well-posedness results to the case involving Faraday’s law, which in particular allows us to improve the regularity property of the electric field in the weak existence result.

scholarly journals An age-dependent population equation with diffusion and delayed birth process

2005 ◽  
Vol 2005 (20) ◽  
pp. 3273-3289 ◽  
Author(s):  
G. Fragnelli
Keyword(s):  
Asymptotic Behavior ◽  
Semigroup Theory ◽  
New Age ◽  
Well Posedness ◽  
Birth Process ◽  
Age Dependent ◽  
Population Equation

We propose a new age-dependent population equation which takes into account not only a delay in the birth process, but also other events that may take place during the time between conception and birth. Using semigroup theory, we discuss the well posedness and the asymptotic behavior of the solution.

Feedback theory to the well-posedness of evolution equations

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190616
Author(s):  
S. Boulite ◽  
S. Hadd ◽  
L. Maniar
Keyword(s):  
Evolution Equations ◽  
Semigroup Theory ◽  
Well Posedness ◽  
Boundary Problems ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Research Activities ◽  
Semigroup Approach ◽  
History Of ◽  
And Control

In this paper, we cross the boundary between semigroup theory and general infinite-dimensional systems to bridge the isolated research activities in the two areas. Indeed, we first give a chronological history of the development of the semigroup approach for control theory. Second, we use the feedback theory to prove the well-posedness of a class of dynamic boundary problems. Third, the obtained results are applied to the well-posedness of neutral equations with non-autonomous past. We will also see that the strong connection between semigroup and control theories lies in feedback theory, where different kinds of perturbations appear. This article is part of the theme issue ‘Semigroup applications everywhere’.

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