  The existence and uniqueness of solution to a one-dimensional hyperbolic
integro-differential problem arising in viscoelasticity is here considered. The
kernel, in the linear viscoelasticity equation, represents the relaxation
function which is characteristic of the considered material. Specifically, the
case of a kernel, which does not satisfy the classical regularity requirements
is analysed. This choice is suggested by applications according to the
literature to model a wider variety of materials. A notable example of kernel,
not satisfying the classical regularity requirements, is represented by a wedge
continuous function. Indeed, the linear integro-differential viscoelasticity
equation, characterised by a suitable wedge continuous relaxation function, is
shown to give the classical linear wave equation via a limit procedure.
