New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

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 I2M - Institut de Mathématiques de Marseille
3 Universidad de Sevilla = University of Seville
4 Instituto de Matematicas

We consider the null controllability problem for two coupled parabolic equations with a space-depending coupling term. We analyze both boundary and distributed null controllabil-ity. In each case, we exhibit a minimal time of control, that is to say, a time T0 ∈ [0, ∞] such that the corresponding system is null controllable at any time T > T0 and is not if T < T0. In the distributed case, this minimal time depends on the relative position of the control interval and the support of the coupling term. We also prove that, for a fixed control interval and a time τ0 ∈ [0, ∞], there exist coupling terms such that the associated minimal time is τ0.

Mots clés: Parabolic Systems; control

Domaines: Equations aux dérivées partielles [math.AP]

Farid Ammar Khodja, Assia Benabdallah, Manuel González-Burgos, Luz de Teresa. New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence. Journal of Mathematical Analysis and Applications, 2016, Volume 444 (Issue 2), pp.1071-1113. ⟨hal-01165713⟩