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 $I\subset \subset R$, and the first equation is controlled by a force supported in a subinterval of $I$ 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

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@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}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016061}, mrnumber = {3716929}, zbl = {1375.93018}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.numdam.org/articles/10.1051/cocv/2016061/ %R 10.1051/cocv/2016061 %G en %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, Volume 23 (2017) no. 4, pp. 1473-1498. doi : 10.1051/cocv/2016061. http://archive.numdam.org/articles/10.1051/cocv/2016061/

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