This Note is concerned with the boundary controllability of non-scalar linear parabolic systems. More precisely, two coupled one-dimensional linear parabolic equations are considered. We show that, with boundary controls, the situation is much more complex than for similar distributed control systems. In our main result, we provide necessary and sufficient conditions for null controllability.
Cette Note concerne la contrôlabilité frontière des systèmes paraboliques linéaires non scalaires. Plus précisement, on considère un système de deux équations paraboliques linéaires de dimension 1 en espace. Nous montrons qu'il est beaucoup plus compliqué de contrôler sur une partie du bord que de le faire avec des contrôles distribués. Dans notre résultat principal, on donne des conditions nécessaires et suffisantes pour la contrôlabilité exacte à zéro.
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@article{CRMATH_2009__347_13-14_763_0, author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and de Teresa, Luz}, title = {On the boundary controllability of non-scalar parabolic systems}, journal = {Comptes Rendus. Math\'ematique}, pages = {763--766}, publisher = {Elsevier}, volume = {347}, number = {13-14}, year = {2009}, doi = {10.1016/j.crma.2009.04.020}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.04.020/} }
TY - JOUR AU - Fernández-Cara, Enrique AU - González-Burgos, Manuel AU - de Teresa, Luz TI - On the boundary controllability of non-scalar parabolic systems JO - Comptes Rendus. Mathématique PY - 2009 SP - 763 EP - 766 VL - 347 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.04.020/ DO - 10.1016/j.crma.2009.04.020 LA - en ID - CRMATH_2009__347_13-14_763_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A González-Burgos, Manuel %A de Teresa, Luz %T On the boundary controllability of non-scalar parabolic systems %J Comptes Rendus. Mathématique %D 2009 %P 763-766 %V 347 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.04.020/ %R 10.1016/j.crma.2009.04.020 %G en %F CRMATH_2009__347_13-14_763_0
Fernández-Cara, Enrique; González-Burgos, Manuel; de Teresa, Luz. On the boundary controllability of non-scalar parabolic systems. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 763-766. doi : 10.1016/j.crma.2009.04.020. http://www.numdam.org/articles/10.1016/j.crma.2009.04.020/
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