Exponential decay of solutions to an inertial model for a wave equation with viscoelastic damping and time varying delay

Abstract

In the present work, we study the global existence and uniform decay rates of solutions to the initial-boundary value problem related to  the dynamic behavior of evolution equations accounting for rotational inertial forces along with a linear time-nonlocal Kelvin-Voigt  damping arising in viscoelastic materials. By constructing appropriate Lyapunov functional, we show that the solution converges to the  equilibrium state exponentially in the energy space.