In this paper, we study the optimal time problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. To begin with, we build an exact solution. The dependence of this solution as regards the scaling parameter naturally opens the way to study the existence and uniqueness of an optimal time control. If, moreover, one assumes the null controllability, it enables to establish a bang-bang type property.
Mots-clés : Optimal time control problem, null controllability, bang-bang property, heat equation, Scaling parameter
@article{RO_2017__51_4_1289_0,
author = {Benalia, Karim and David, Claire and Oukacha, Brahim},
title = {An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1289--1299},
publisher = {EDP-Sciences},
volume = {51},
number = {4},
year = {2017},
doi = {10.1051/ro/2017006},
mrnumber = {3783945},
zbl = {1393.35070},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2017006/}
}
TY - JOUR AU - Benalia, Karim AU - David, Claire AU - Oukacha, Brahim TI - An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 1289 EP - 1299 VL - 51 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2017006/ DO - 10.1051/ro/2017006 LA - en ID - RO_2017__51_4_1289_0 ER -
%0 Journal Article %A Benalia, Karim %A David, Claire %A Oukacha, Brahim %T An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 1289-1299 %V 51 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2017006/ %R 10.1051/ro/2017006 %G en %F RO_2017__51_4_1289_0
Benalia, Karim; David, Claire; Oukacha, Brahim. An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1289-1299. doi : 10.1051/ro/2017006. http://www.numdam.org/articles/10.1051/ro/2017006/
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