Global existence and energy decay of solutions to a viscoelastic Timoshenko beam system with a nonlinear delay term

Abstract

In this paper, we consider the viscoelastic Timoshenko beam system with a delay term in the weakly nonlinear internal feedback in a bounded domain:

We prove a global existence result using the energy method combined with the Faedo- Galerkin procedure under a condition between the weight of delay term in the feedback and the weight of the term without delay. Furthermore, we study the asymptotic behavior of solutions using a perturbed energy method.

Keywords:

• Timoshenko beam system
• viscoelastic term
• delay term
• decay rate
• Lyapunov functionals

AMS Subject Classifications:

• 35B40
• 35L70
• 49K25
• 93D15

Acknowledgements

We would like to thank very much the referees for their important remarks and comments which allow us to correct and improve this paper.

Notes

No potential conflict of interest was reported by the authors.