Analysis of the energy decay of a viscoelasticity type equation

In this paper, we study the evolution of the energy density of a sequence of solutions of a problem related to a viscoelasticity model where the viscosity term is a pseudo-differential operator of order 2α with α ∈ (0, 1). We calculate the weak limit of the energy density in terms of microlocal defect measures and under special assumption we prove that the viscosity term prevents propagation of concentration and oscillation effects contrary to what happens in the wave equation.