We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.
Mots clés : parabolic equation, approximate controllability, multiplicative controls, nonnegative locally distributed controls
@article{COCV_2012__18_4_1207_0,
author = {Fern\'andez, Luis Alberto and Khapalov, Alexander Yuri},
title = {Controllability properties for the one-dimensional {Heat} equation under multiplicative or nonnegative additive controls with local mobile support},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1207--1224},
publisher = {EDP-Sciences},
volume = {18},
number = {4},
year = {2012},
doi = {10.1051/cocv/2012004},
mrnumber = {3019478},
zbl = {1262.35119},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2012004/}
}
TY - JOUR AU - Fernández, Luis Alberto AU - Khapalov, Alexander Yuri TI - Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 1207 EP - 1224 VL - 18 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012004/ DO - 10.1051/cocv/2012004 LA - en ID - COCV_2012__18_4_1207_0 ER -
%0 Journal Article %A Fernández, Luis Alberto %A Khapalov, Alexander Yuri %T Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 1207-1224 %V 18 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012004/ %R 10.1051/cocv/2012004 %G en %F COCV_2012__18_4_1207_0
Fernández, Luis Alberto; Khapalov, Alexander Yuri. Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1207-1224. doi : 10.1051/cocv/2012004. http://www.numdam.org/articles/10.1051/cocv/2012004/
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