scholarly journals Stability result of the Lamé system with a delay term in the internal fractional feedback

2021 ◽  
Vol 13 (2) ◽  
pp. 336-355
Author(s):  
Abbes Benaissa ◽  
Soumia Gaouar
Keyword(s):  
Exponential Stability ◽  
Existence And Uniqueness ◽  
Semigroup Theory ◽  
Stability Result ◽  
Classical Theorem ◽  
Uniqueness Of Solutions ◽  
Delay Term ◽  
Lamé System ◽  
Lame System

Abstract In this article, we consider a Lamé system with a delay term in the internal fractional feedback. We show the existence and uniqueness of solutions by means of the semigroup theory under a certain condition between the weight of the delay term in the fractional feedback and the weight of the term without delay. Furthermore, we show the exponential stability by the classical theorem of Gearhart, Huang and Pruss.

scholarly journals Existence, Uniqueness, and Almost Sure Exponential Stability of Solutions to Nonlinear Stochastic System with Markovian Switching and Lévy Noises

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Chao Wei
Keyword(s):  
Exponential Stability ◽  
Stochastic System ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Nonlinear Stochastic System ◽  
Stability Of Solutions ◽  
Uniqueness Of Solutions ◽  
Almost Sure Exponential Stability

This paper is concerned with existence, uniqueness, and almost sure exponential stability of solutions to nonlinear stochastic system with Markovian switching and Lévy noises. Firstly, the existence and uniqueness of solutions to the system is studied. Then, the almost sure exponential stability of the system is derived. Finally, an example is presented to illustrate the results.

scholarly journals Uniform stability for a type III thermoelastic laminated beam with structural damping

2022 ◽  
Author(s):  
Fayssal Djellali
Keyword(s):  
Heat Flux ◽  
Exponential Stability ◽  
Semigroup Theory ◽  
Stability Result ◽  
Uniform Stability ◽  
Well Posedness ◽  
Structural Damping ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Lack Of Exponential Stability

In this work, we consider a thermoelastic laminated beam with structural damping, where the heat flux is given by Green and Naghdi theories. We establish the well-posedness of the system using semigroup theory. Moreover, under the condition of equal wave speeds, we prove an exponential stability result for the considered system. In the case of lack of exponential stability we show that the solution decays polynomially.

scholarly journals The Exponential Stability Result of an Euler-Bernoulli Beam Equation with Interior Delays and Boundary Damping

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Peng-cheng Han ◽  
Yan-fang Li ◽  
Gen-qi Xu ◽  
Dan-hong Liu
Keyword(s):  
Exponential Stability ◽  
Semigroup Theory ◽  
Stability Result ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Boundary Damping ◽  
Exponentially Stable ◽  
Stability Issue ◽  
Euler Bernoulli Beam ◽  
The Relationship

We study the exponential stability of Euler-Bernoulli beam with interior time delays and boundary damping. At first, we prove the well-posedness of the system by the C0 semigroup theory. Next we study the exponential stability of the system by constructing appropriate Lyapunov functionals. We transform the exponential stability issue into the solvability of inequality equations. By analyzing the relationship between delays parameters α and damping parameters β, we describe (β,α)-region for which the system is exponentially stable. Furthermore, we obtain an estimation of the decay rate λ⁎.

scholarly journals An analysis on the stability of a state dependent delay differential equation

2016 ◽  
Vol 14 (1) ◽  
pp. 425-435 ◽  
Author(s):  
Sertaç Erman ◽  
Ali Demir
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Delay Term ◽  
State Dependent ◽  
State Dependent Delay ◽  
The Stability ◽  
Delay Differential ◽  
Equation With Delay

AbstractIn this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term $\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

Existence and uniqueness result for an hyperbolic scalar conservation law with a stochastic force using a finite volume approximation

2020 ◽  
Vol 17 (02) ◽  
pp. 213-294
Author(s):  
Caroline Bauzet ◽  
Vincent Castel ◽  
Julia Charrier
Keyword(s):  
Finite Volume ◽  
Existence And Uniqueness ◽  
Entropy Solution ◽  
Stability Result ◽  
Uniqueness Result ◽  
Finite Volume Scheme ◽  
Uniqueness Of Solutions ◽  
Stochastic Force ◽  
Scalar Conservation Law ◽  
Scalar Conservation

We are interested in multi-dimensional nonlinear scalar conservation laws forced by a multiplicative stochastic noise with a general time and space dependent flux-function. We address simultaneously theoretical and numerical issues in a general framework and consider a larger class of flux functions in comparison to the one in the literature. We establish existence and uniqueness of a stochastic entropy solution together with the convergence of a finite volume scheme. The novelty of this paper is the use of a numerical approximation (instead of a viscous one) in order to get, both, the existence and the uniqueness of solutions. The quantitative bounds in our uniqueness result constitute a preliminary step toward the establishment of strong error estimates. We also provide an [Formula: see text] stability result for the stochastic entropy solution.

Exponential stability for a thermoelastic laminated beam with nonlinear weights and time-varying delay

2021 ◽  
pp. 1-29
Author(s):  
Carlos Nonato ◽  
Carlos Raposo ◽  
Baowei Feng
Keyword(s):  
Exponential Stability ◽  
Existence And Uniqueness ◽  
Semigroup Theory ◽  
Well Posedness ◽  
Time Varying ◽  
Structural Damping ◽  
Laminated Beam ◽  
Time Varying Delay ◽  
Timoshenko Systems ◽  
Varying Delay

In this paper, we study the well-posedness and asymptotic stability to a thermoelastic laminated beam with nonlinear weights and time-varying delay. To the best of our knowledge, there are no results on the system and related Timoshenko systems with nonlinear weights. On suitable premises about the time delay and the hypothesis of equal-speed wave propagation, existence and uniqueness of solution is obtained by combining semigroup theory with Kato variable norm technique. The exponential stability is proved by energy method in two cases, with and without the structural damping, by using suitably sophisticated estimates for multipliers to construct an appropriated Lyapunov functional.

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.

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