Asymptotic behavior of solutions for the nonlinear hyperbolic equation with an external time delay

In this talk, we introduce some behavior of solutions to the nonlinear hyperbolic equation with an external time delay. The system is also considered some complex space concerning electricity. First, we introduce the main theorem and some lemmas. We also the smallness condition and taking into account the appropriate Lyapunov functional. Finally, we get the energy decay rate of the main energy for the system.