Null-controllability of non-autonomous Ornstein-Uhlenbeck equations

Karine Beauchard (1, 2) , Karel Pravda-Starov (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ENS Rennes - École normale supérieure - Rennes

We study the null-controllability of parabolic equations associated to non-autonomous Ornstein-Uhlenbeck operators. When a Kalman type condition holds for some positive time $T>0$, these parabolic equations are shown to enjoy a Gevrey regularizing effect at time $T>0$. Thanks to this regularizing effect, we prove by adapting the Lebeau-Robbiano method that these parabolic equations are null-controllable in time greater than or equal to $T>0$ from control regions, for which null-controllability is classically known to hold in the case of the heat equation.

Mots clés: Null-controllability; Observability; non-autonomous Ornstein-Uhlenbeck operators; Gevrey regularity; Kalman type condition

Domaines: Equations aux dérivées partielles [math.AP]

Karine Beauchard, Karel Pravda-Starov. Null-controllability of non-autonomous Ornstein-Uhlenbeck equations. Journal of Mathematical Analysis and Applications, 2017, 456 (1), pp.496-524. ⟨10.1080/0023131.2017.07.014⟩. ⟨hal-01355812⟩