Rational stabilization of the multidimensional wave equation with dynamical control and time-varying delay

We consider the multidimensional wave equation with a time-varying delay term in the dynamical control. Under suitable assumptions, we show the well posedness of the problem. These results are obtained by using semi-group theory. Using direct computations, through the multiplier method, the rational energy decay rate of the system will be given according to the regularity of the initial data.