Global existence and exponential stability for a nonlinear Timoshenko system with delay

Abstract

This paper is concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with time delay. The delay is defined on a feedback term associated to the equation for rotation angle. Under suitable assumptions on the data, we establish the well-posedness of the problem with respect to weak solutions. We also establish the exponential stability of the system under the usual equal wave speeds assumption. MSC: 35B40

Exponential Stability for a Nonlinear Timoshenko System with Distributed Delay

“…In [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] investigated a thermo-elastic system of Timoshenko type with second sound and distributed delay (1.5) In the present work, we extend the result of Feng and Pelier, [6] where constant delay is replaced by distributed delay.…”

Global existence and stability results for a nonlinear Timoshenko system of thermoelasticity of type III with delay

“…By using the same methods as those in [15] and in [16], we can obtain the following Lemmas 3.1 and 3.2, respectively. We omit the proof.…”

“…The construction of the auxiliary function I 1 (t) -I 3 (t), I 5 (t) comes from [16]. (φ, ψ, θ , z) be the solution of (2.4).…”

“…Feng and Pelicer [16] obtained an exponential stability under equal wave speeds. In the present paper, when…”

“…In Sect. 3, we establish the well-posedness of system (1.1)-(1.2) by using semigroup theory in [15,16]. In Sect.…”