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.

Mathematics Subject Classification (2020):

• 35A01
• 37L65
• 93C20
• 93D15

Key words:

• Global existence
• Faedo-Galerkin method
• relaxation function
• viscoelasticity