Ыpectral analysis of linear models of viscoelasticity

In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity, as Gurtin–Pipkin integrodifferential equations that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law).