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.

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