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

TL;DR

This paper develops a method to identify a space-varying coefficient in a linear viscoelastic string model with memory, extending existing approaches to systems with persistent memory using a generalized Blagoveshchenskii equation.

Contribution

It extends a dynamical identification approach to viscoelastic systems with memory, introducing a generalized Blagoveshchenskii equation for this class.

Findings

Successfully extended the Blagoveshchenskii equation to systems with memory

Provided a new identification method for space-varying coefficients in viscoelastic models

Demonstrated the approach on a Maxwell-Boltzmann type string

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.