General decay properties of abstract linear viscoelasticity

We consider a linear Volterra integro-differential equation of hyperbolic type, which can be viewed as an abstract version of the equation ∂ttu(t)-Δu(t)+∫0tμ(s)Δu(t-s)ds=0describing the motion of linearly viscoelastic solids. We establish some decay results for the associated energy, under assumptions that do not involve differential inequalities for the convolution kernel μ.