In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are -periodic and of size . We show that, as , the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion of material in the perforated domain and is equal to 1 when there are no holes. We also prove that the solution of the approximate controllability problem in the perforated domain behaves, as , as that of the problem posed in the perforated domain having as rigth-hand side the (fixed) control of the limit problem.
Mots clés : linear parabolic equation, approximate controlability, homogenization
@article{COCV_2001__6__21_0,
author = {Donato, Patrizia and Nabil, A{\"\i}ssam},
title = {Approximate controllability of linear parabolic equations in perforated domains},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {21--38},
publisher = {EDP-Sciences},
volume = {6},
year = {2001},
mrnumber = {1804496},
zbl = {0964.35015},
language = {en},
url = {http://www.numdam.org/item/COCV_2001__6__21_0/}
}
TY - JOUR AU - Donato, Patrizia AU - Nabil, Aïssam TI - Approximate controllability of linear parabolic equations in perforated domains JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2001 SP - 21 EP - 38 VL - 6 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_2001__6__21_0/ LA - en ID - COCV_2001__6__21_0 ER -
%0 Journal Article %A Donato, Patrizia %A Nabil, Aïssam %T Approximate controllability of linear parabolic equations in perforated domains %J ESAIM: Control, Optimisation and Calculus of Variations %D 2001 %P 21-38 %V 6 %I EDP-Sciences %U http://www.numdam.org/item/COCV_2001__6__21_0/ %G en %F COCV_2001__6__21_0
Donato, Patrizia; Nabil, Aïssam. Approximate controllability of linear parabolic equations in perforated domains. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 21-38. http://www.numdam.org/item/COCV_2001__6__21_0/
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