Volume 23, Number 4, October-December 2017
|Page(s)||1649 - 1666|
|Published online||21 September 2017|
Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type∗
Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy .
Received: 15 May 2015
Revised: 26 May 2016
Accepted: 5 October 2016
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.
Mathematics Subject Classification: 45K05 / 93B03 / 93B05 / 93C22
Key words: Controllability / systems with persistent memory / viscoelasticity
© EDP Sciences, SMAI 2017
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