Controllability of isotropic viscoelastic bodies of Maxwell-Boltzmann type
For researchers in control theory and continuum mechanics, this extends known controllability results from elastic to viscoelastic materials, but the approach is incremental.
The paper proves that a three-dimensional isotropic viscoelastic body of Maxwell-Boltzmann type inherits the controllability properties of the corresponding purely elastic system when controlled on part of the boundary.
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.