We consider an electrically conducting 2-D channel fluid flow affected by a transverse magnetic field. The governing equations are the magnetohydrodynamics equations. We design an explicit finite-dimensional exponentially stabilizing feedback, given in a very simple form, easily manageable from the computational point of view, for the Hartmann−Poiseuille profile. Moreover, the stability is assured independently of the value of the magnetic Reynolds number. The control acts on the normal components of both velocity and magnetic field, on the upper wall only.
DOI : 10.1051/cocv/2016025
Mots-clés : Magnetohydrodynamics equations, Hartmann-Poiseuille profile, stabilization, feedback controller, eigenvalues
@article{COCV_2017__23_4_1253_0,
author = {Ionu\c{t} Munteanu},
title = {Boundary stabilization of a {2-D} periodic {MHD} channel flow, by proportional feedbacks},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1253--1266},
publisher = {EDP-Sciences},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016025},
zbl = {1375.76217},
mrnumber = {3716920},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2016025/}
}
TY - JOUR AU - Ionuţ Munteanu TI - Boundary stabilization of a 2-D periodic MHD channel flow, by proportional feedbacks JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1253 EP - 1266 VL - 23 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016025/ DO - 10.1051/cocv/2016025 LA - en ID - COCV_2017__23_4_1253_0 ER -
%0 Journal Article %A Ionuţ Munteanu %T Boundary stabilization of a 2-D periodic MHD channel flow, by proportional feedbacks %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1253-1266 %V 23 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016025/ %R 10.1051/cocv/2016025 %G en %F COCV_2017__23_4_1253_0
Ionuţ Munteanu. Boundary stabilization of a 2-D periodic MHD channel flow, by proportional feedbacks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1253-1266. doi : 10.1051/cocv/2016025. http://www.numdam.org/articles/10.1051/cocv/2016025/
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