Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects
Abstract
We analyse the controllability problem for a one-dimensional heat equation involving the fractional Laplacian $(-d_x^{\,2})^{s}$ on the interval $(-1,1)$. Using classical results and techniques, we show that, acting from an open subset $\omega \subset (-1,1)$, the problem is null-controllable for $s>1/2$ and that for $s\leqslant 1/2$ we only have approximate controllability. Moreover, we deal with the numerical computation of the control employing the penalized Hilbert Uniqueness Method and a finite element scheme for the approximation of the solution to the corresponding elliptic equation. We present several experiments confirming the expected controllability properties.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 06, 2018
- Source ID
- 10.1093/imamci/dny025
Entities
People
- Umberto Biccari
- Víctor Hernández-santamaría
Organizations
- Air Force Office of Scientific Research
- European Research Council
- Ministry of Economy, Industry and Competitiveness
- University of Deusto