Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function

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 \mu/\delta^2, defined on a bounded C^2 domain \Omega\subsetR^N, 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.

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