Stabilization for solutions of plate equation with time-varying delay and weak-viscoelasticity in $\mathbb{R}^n$

We consider a dynamical system with delay described by a differential equation with partial derivatives of hyperbolic type and delay with respect to a time variable. We establish in Theorem 3.1 the $k(t)$-stability of weak solution under suitable initial conditions in $\mathbb{R}^n, n>4$ by introducing an appropriate Lyapunov functions.