Null controllability results for parabolic equations in unbounded domains

Abstract

In this talk we present some results concerning the null controllability for a heat equation in unbounded domains. We characterize the conditions that must satisfy the weight function, introduced by Fursikov and Imanuvilov, in order to prove a global Carleman inequality for the adjoint problem and then to get a null controllability result. We give some examples of unbounded domains (Ω, ω) that satisfy these sufficient conditions. Finally, when Ω \ ω is bounded, we prove the null controllability of the semi-linear heat equation when the nonlinearity is slightly superlinear.