Geodesic
Boundary stabilization of a 2-D periodic MHD channel flow, by proportional feedbacks
Ionuţ Munteanu1
1 Alexandru Ioan Cuza University, Department of Mathematics, and Octav Mayer Institute of Mathematics (Romanian Academy), Bvd. Carol I no. 11, 700506 Iaşi, Romania.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1253-1266

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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.

Reçu le :
DOI : 10.1051/cocv/2016025
Classification : 76W05, 93D15, 93B60
Keywords: Magnetohydrodynamics equations, Hartmann-Poiseuille profile, stabilization, feedback controller, eigenvalues

Ionuţ Munteanu 1

1 Alexandru Ioan Cuza University, Department of Mathematics, and Octav Mayer Institute of Mathematics (Romanian Academy), Bvd. Carol I no. 11, 700506 Iaşi, Romania. 
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     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},
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     year = {2017},
     doi = {10.1051/cocv/2016025},
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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

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