Materials with memory, namely those materials whose mechanical and/or
thermodynamical behaviour depends on time not only via the present time, but
also through its past history, are considered. Specifically, a three
dimensional viscoelastic body is studied. Its mechanical behaviour is described
via an integro-differential equation, whose kernel represents the relaxation
modulus, characteristic of the viscoelastic material under investigation.
According to the classical model, to guarantee the thermodynamical
compatibility of the model itself, such a kernel satisfies regularity
conditions which include the integrability of its time derivative. To adapt the
model to a wider class of materials, this condition is relaxed; that is,
conversely to what is generally assumed, no integrability condition is imposed
on the time derivative of the relaxation modulus. Hence, the case of a
relaxation modulus which is unbounded at the initial time t = 0, is considered,
so that a singular kernel integro-differential equation, is studied. In this
framework, the existence of a weak solution is proved in the case of a three
dimensional singular kernel initial boundary value problem.Comment: 15 page
