This paper is devoted to the controllability of linear systems of two coupled parabolic equations when the coupling involves a space dependent first order term. This system is set on an bounded interval , and the first equation is controlled by a force supported in a subinterval of or on the boundary. In the case where the intersection of the coupling and control domains is nonempty, we prove null controllability at any time. Otherwise, we provide a minimal time for null controllability. Finally we give a necessary and sufficient condition for the approximate controllability. The main technical tool for obtaining these results is the moment method.
Keywords: Controllability, observability, moment method, parabolic systems
Duprez, Michel 1
@article{COCV_2017__23_4_1473_0,
author = {Duprez, Michel},
title = {Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1473--1498},
year = {2017},
publisher = {EDP Sciences},
volume = {23},
number = {4},
doi = {10.1051/cocv/2016061},
mrnumber = {3716929},
zbl = {1375.93018},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016061/}
}
TY - JOUR
AU - Duprez, Michel
TI - Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2017
SP - 1473
EP - 1498
VL - 23
IS - 4
PB - EDP Sciences
UR - https://www.numdam.org/articles/10.1051/cocv/2016061/
DO - 10.1051/cocv/2016061
LA - en
ID - COCV_2017__23_4_1473_0
ER -
%0 Journal Article
%A Duprez, Michel
%T Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2017
%P 1473-1498
%V 23
%N 4
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/cocv/2016061/
%R 10.1051/cocv/2016061
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%F COCV_2017__23_4_1473_0
Duprez, Michel. Controllability of a $2 \times{} 2$ parabolic system by one force with space-dependent coupling term of order one. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1473-1498. doi: 10.1051/cocv/2016061
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