# Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential

U. Biccari Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential, Math. Control Relat. F., Vol. 9, No. 1 (2019), pp. 191-219, DOI: 10.3934/mcrf.2019011

Abstract: We analyse controllability properties for the one-dimensional heat equation with singular inverse-square potential u_t-u_{xx}-\frac{\mu}{x^2}u=0\,\,\,(x,t)\in(0,1)\times(0,T) . For any \mu <1/4 , we prove that the equation is null controllable through a boundary control f\in H^1(0,T) acting at the singularity point x=0 . This result is obtained employing the moment method by Fattorini and Russell.