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In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
@article{COCV_2013__19_4_1209_0,
author = {Cornilleau, Pierre and Guerrero, Sergio},
title = {On the cost of null-control of an artificial advection-diffusion problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1209--1224},
publisher = {EDP-Sciences},
volume = {19},
number = {4},
year = {2013},
doi = {10.1051/cocv/2013048},
mrnumber = {3182686},
zbl = {1293.35021},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013048/}
}
TY - JOUR AU - Cornilleau, Pierre AU - Guerrero, Sergio TI - On the cost of null-control of an artificial advection-diffusion problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1209 EP - 1224 VL - 19 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013048/ DO - 10.1051/cocv/2013048 LA - en ID - COCV_2013__19_4_1209_0 ER -
%0 Journal Article %A Cornilleau, Pierre %A Guerrero, Sergio %T On the cost of null-control of an artificial advection-diffusion problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1209-1224 %V 19 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013048/ %R 10.1051/cocv/2013048 %G en %F COCV_2013__19_4_1209_0
Cornilleau, Pierre; Guerrero, Sergio. On the cost of null-control of an artificial advection-diffusion problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1209-1224. doi: 10.1051/cocv/2013048
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