**Biccari U., Zuazua E.** Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function

Journal of Differential Equations, 261 (2016) 2809–2853 ,DOI: 10.1016/j.jde.2016.05.019

**Abstract:** This article is devoted to the analysis of control properties for a heat equation with a singular potential , defined on a bounded domain , where δ is the distance to the boundary function. More precisely, we show that for any μ≤1/4 the system is exactly null controllable using a distributed control located in any open subset of Ω, while for μ>1/4 there is no way of preventing the solutions of the equation from blowing-up. The result is obtained applying a new Carleman estimate.