Decay of Solution for Degenerate Wave Equation of Kirchhoff Type in Viscoelasticity

Abstract

In this paper we consider a class of degenerate viscoelastic wave equation with density in Kirchhoff-type. Under appropriate conditions on the initial datums, we prove a very general decay rate of solution using the Lyapunov functions. In order to compensate the lack of Poincare’s inequality in $$\mathbb {R}^{n}$$ , we use spaces weighted by density function.