# American Institute of Mathematical Sciences

March  2017, 22(2): 491-506. doi: 10.3934/dcdsb.2017024

## Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks

 Laboratory ACEDP, Djillali Liabes university, 22000 Sidi Bel Abbes, Algeria

* Corresponding author: hakemali@yahoo.com

Received  October 2015 Revised  October 2016 Published  December 2016

Fund Project: The authors are supported by CNEPRU-ALGERIA.

In this paper, we investigate the nonlinear wave equation in a bounded domain with a time-varying delay term in the weakly nonlinear internal feedback
 $\left(|u_{t}|^{\gamma-2}u_{t}\right)_{t}-Lu-\int_{0}^{t}g(t-s)L u(s)ds+ \mu_{1} \psi(u_{t}(x, t))+ \mu_{2} \psi(u_{t}(x, t-\tau(t)))=0.$
The asymptotic behavior of solutions is studied by using an appropriate Lyapunov functional. Moreover, we extend and improve the previous results in the literature.
Citation: Ferhat Mohamed, Hakem Ali. Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 491-506. doi: 10.3934/dcdsb.2017024
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