Control of the Grushin equation: non-rectangular control region and minimal time

Michel Duprez (1) , Armand Koenig (2)

1 I2M - Institut de Mathématiques de Marseille
2 LJAD - Laboratoire Jean Alexandre Dieudonné

This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control region. We establish the positive result thanks to the fictitious control method and the negative one by interpreting the associated observability inequality as an $L^2$ estimate on complex polynomials.

Domaines: Equations aux dérivées partielles [math.AP]

Michel Duprez, Armand Koenig. Control of the Grushin equation: non-rectangular control region and minimal time. ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, pp.3. ⟨10.1051/cocv/2019001⟩. ⟨hal-01829294v2⟩