On Exponential Asymptotic Stability in Linear Viscoelasticity

This paper establishes results concerning the exponential decay of strong solutions of a linear hyperbolic integrodifferential equation in Hilbert space. Rather than the more commonly used assumptions that the relaxation function is non-negative, decreasing and convex, dissipation is modelled by requiring that the dynamic viscosity be a positive function. This restriction has a firm thermodynamic basis. Frequency domain methods are employed.