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 (. 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.
Accepté le :
DOI : 10.1051/cocv/2016068
Mots clés : Controllability, systems with persistent memory, viscoelasticity
@article{COCV_2017__23_4_1649_0,
author = {Pandolfi, L.},
title = {Controllability of isotropic viscoelastic bodies of {Maxwell{\textendash}Boltzmann} type},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1649--1666},
publisher = {EDP-Sciences},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016068},
zbl = {1398.93048},
mrnumber = {3716936},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2016068/}
}
TY - JOUR AU - Pandolfi, L. TI - Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1649 EP - 1666 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016068/ DO - 10.1051/cocv/2016068 LA - en ID - COCV_2017__23_4_1649_0 ER -
%0 Journal Article %A Pandolfi, L. %T Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1649-1666 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016068/ %R 10.1051/cocv/2016068 %G en %F COCV_2017__23_4_1649_0
Pandolfi, L. Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1649-1666. doi : 10.1051/cocv/2016068. http://archive.numdam.org/articles/10.1051/cocv/2016068/
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