Decay rate of solutions to the Cauchy problem for a coupled system of viscoelastic wave equations with a strong delay in Rⁿ

Abstract

"Using weighted spaces, we establish a general decay rate properties of solutions as T → ∞ for a coupled system of viscoelastic wave equations in Rⁿ under some conditions on g1, g2, φ. We exploit a density function to introduce weighted spaces for solutions and using an appropriate Lyapunov function. Keywords: Lyapunov function, relaxation function, density, decay rate, weighted spaces."