  In this paper we solve the problem of the identification of a coefficient
which appears in the model of a distributed system with persistent memory
encountered in linear viscoelasticity (and in diffusion processes with memory).
The additional data used in the identification are subsumed in the input output
map from the deformation to the traction on the boundary. We extend a dynamical
approach to identification introduced by Belishev in the case of purely elastic
(memoryless) bodies and based on a special equation due to Blagoveshchenskii.
So, in particular, we extend Blagoveshchenskii equation to our class of systems
with persistent memory.
