Tijani A. Apalara

Asymptotic behavior of weakly dissipative Timoshenko system with internal constant delay feedbacks

In this paper, we consider a one-dimensional Timoshenko system with a linear frictional damping and a constant delay acting on the displacement equation. Under appropriate assumptions on the weight of the delay and the wave speeds, we establish the well posedness and asymptotic stability results of the system. Our stability results show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.

A stability result for the vibrations given by the standard linear model with thermoelasticity of type III

Abstract The aim of this article is to establish the well-posedness as well as an exponential stability result for the standard linear solid vibrating systems of thermoelasticity type III. Numerical experiments using finite differences are given to confirm our analytical result.