Controllability of isotropic viscoelastic bodies of Maxwell-Boltzmann type

TL;DR

This paper demonstrates that a three-dimensional isotropic Maxwell-Boltzmann type viscoelastic body retains the controllability characteristics of its elastic counterpart, using advanced mathematical techniques.

Contribution

It establishes the controllability of viscoelastic bodies of Maxwell-Boltzmann type, extending known results from elastic systems through cosine operator and moment theory methods.

Findings

Viscoelastic body inherits elastic controllability properties.

Controllability proven using cosine operator and moment theory.

Results applicable to boundary-controlled 3D isotropic bodies.

Abstract

In this paper we consider a viscoelastic three dimensional body (of Maxwell-Boltzmann type) controlled on (part of) the boundary. We assume that the material is isotropic and homogeneous. If the body is elastic (i.e. no dissipation due to past memory), controllability has been studied by several authors. We prove that the viscoelastic body inherits the controllability properties of the corresponding purely elastic system. The proof relays on cosine operator methods combined with moment theory.