Boundary approximate controllability of some linear parabolic systems

Guillaume Olive (1)

1 analyse appliquée

This paper focuses on the boundary approximate controllability of two classes of linear parabolic systems, namely a system of n heat equations coupled through constant terms and a 2x2 cascade system coupled by means of a fi rst order partial diff erential operator with space-dependent coe fficients. For each system we prove a suffi cient condition in any space dimension and we show that this condition turns out to be also necessary in one dimension with only one control. For the system of coupled heat equations we also study the problem on rectangle, and we give characterizations depending on the position of the control domain. Finally, we exhibit a cascade system for which the distributed controllability holds whereas the boundary controllability does not. The method relies on a general characterization due to H.O. Fattorini.

Mots clés: parabolic systems; boundary controllability; distributed controllability; hautus test

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Guillaume Olive. Boundary approximate controllability of some linear parabolic systems. Evolution Equations and Control Theory, 2014, 3 (1), pp.167-189. ⟨10.3934/eect.2014.3.167⟩. ⟨hal-00808381v2⟩