Null controllability of the heat equation in pseudo-cylinders by an internal control

Jon Asier Bárcena-Petisco (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper we prove the null controllability of the heat equation in domains which have a cylindrical part and which are limited by a Lipschitz graph. The proof consists mainly on getting a Carleman estimate, which presents the usual absorptions properties. In order to face the difficulty that the domain is just Lipschitz, we use its cylindrical structure and approximate the system by the same system stated in regular domains.

Mots clés: Carleman inequalities; heat equation; Lipschitz domains; null controllability

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Jon Asier Bárcena-Petisco. Null controllability of the heat equation in pseudo-cylinders by an internal control. 2019. ⟨hal-02145122v2⟩