# Controllability of the one-dimensional fractional heat equation under positivity constraints

U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Communications on Pure & Applied Analysis (CPAA). (2019) DOI: 10.1137/17M1119160

Abstract: In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian $(-\Delta)^s$ ($01/2$. Moreover, we show that in this minimal time constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. We also give some numerical simulations that confirm our theoretical results.