On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity

Abstract

En
The asymptotic behaviour of a scalar linear nonconvolution Volterra equation is investigated; the equation is that satisfied by the modes of a viscoelastic rod bending quasi-statically. A sufficient condition for the trivial solution to be asymptotic stable is given, as well as results on describing the exact rate of decay: in the case that the trivial solution is unstable, the exact rate of growth of solutions is specified.