Identification of a space varying coefficient of a linear viscoelastic string of Maxwell-Boltzman type

Abstract

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.