DCDS-B
Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks
Ferhat Mohamed Hakem Ali
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.
keywords: Energy decay viscoelastic term time-varying delay term

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