Biccari U., Hernández-Santamaría V. Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, IMA Journal of Mathematical Control and Information DOI: 10.1093/imamci/dny025
Abstract: We analyze the controllability problem for a one-dimensional heat equation involving the fractional Laplacian on the interval . Using classical results and techniques, we show that, acting from an open subset , the problem is null-controllable for and that for we only have approximate controllability. Moreover, we deal with the numerical computation of the control employing the penalized Hilbert Uniqueness Method (HUM) and a finite element (FE) scheme for the approximation of the solution to the corresponding elliptic equation. We present several experiments confirming the expected controllability properties.