Recent results on the controllability of linear coupled parabolic problems: A survey

Farid Ammar-Khodja (1) , Assia Benabdallah (2) , Manuel González-Burgos (3) , Luz de Teresa (4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 Universidad de Sevilla = University of Seville
4 Instituto de Matematicas

This paper tries to summarize recent results on the controllability of systems of (several) parabolic equations. The emphasis is placed on the extension of the Kalman rank condition (for finite dimensional systems of differential equations) to parabolic systems. This question is itself tied with the proof of global Carleman estimates for systems and leads to a wide field of open problems.

Mots clés: parabolic systems; controllability; Kalman condition

Domaines: Equations aux dérivées partielles [math.AP]

Farid Ammar-Khodja, Assia Benabdallah, Manuel González-Burgos, Luz de Teresa. Recent results on the controllability of linear coupled parabolic problems: A survey. Mathematical Control and Related Fields, 2011, 1 (3), pp.267-306. ⟨10.3934/mcrf.2011.1.267⟩. ⟨hal-01305493⟩