HIGH FREQUENCY ANALYSIS OF FAMILIES OF SOLUTIONS TO THE EQUATION OF VISCOELASTICITY OF KELVIN–VOIGT
Amel Atallah-Baraket, Clotilde Fermanian Kammerer · Journal of Hyperbolic Differential Equations · 2004
In this paper, we study the evolution of the energy density of a sequence of solutions to the Kelvin–Voigt viscoelasticity equation. We do not suppose lower bounds on the non-negative viscosity matrix. We prove that, in the zone where the viscosity matrix is invertible, this term prevents propagation of concentation and oscillation effects contrary to what happens in the wave equation. We calculate precisely the weak limit of the energy density in terms of microlocal defect measures associated with the initial data under the assumption that the oscillations of the data are not microlocally localized on directions which are in the kernel of the viscosity matrix.