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

Abstract

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.

Keywords:

• Timoshenko system
• delay
• well posedness
• asymptotic behavior
• equal and non-equal speed propagation

AMS Subject Classifications:

• 35B40
• 35L45
• 74H40
• 93D15
• 93D20

Acknowledgements

The author thanks ACHB-KFUPM for its continuous support and the anonymous referees for their careful reading and valuable suggestions.