Exponential Stability for a Nonlinear Timoshenko System with Distributed Delay

Lamine Bouzettouta ,Fahima Hebhoub ,Karima Ghennam ,Sabrina Benferdi

doi:10.28924/2291-8639-19-2021-77

Lamine Bouzettouta , Fahima Hebhoub + Show 2 more

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https://doi.org/10.28924/2291-8639-19-2021-77

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Abstract

This paper is concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with distributed delay time. The distributed delay is defined on feedback term associated to the equation for rotation angle. Under suitable assumptions on the data, we establish the exponential stability of the system under the usual equal wave speeds assumption.

Highlights

In this work, we consider the following non linear Timoshenko system with distributed delay, (1.1)ρ1φtt − k(φx + ψ)x = 0, ρ2ψtt − bψxx + k(φx + ψ) + μ1ψt + τ2 τ1 μ2(s)ψt(x, t − s)ds f (ψ) =0, where t denotes the time variable and x the space variable along a beam of length 1 in its equilibrium configuration
This paper is concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with distributed delay time
The distributed delay is defined on feedback term associated to the equation for rotation angle

Summary

Introduction

1. Introduction In this work, we consider the following non linear Timoshenko system with distributed delay, (1.1) Timoshenko system, distributed delay time, exponential stability, Lyapunov functional. Result was obtained by the authors when the distributed delay acted on the part of boundary. [11] Mustapha considered a Timoshenko system of thermoelasticity of type III with distributed delay and establish the stability for the case of equal and non equal speeds of wave propagation .Appalara [1]

Results

Conclusion