  We study the symmetric facilitated exclusion process (FEP) on the finite
one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with
boundary reservoirs, whose action is subject to an additional kinetic
constraint in order to enforce ergodicity. We study in details its stationary
states in various settings, and use them in order to derive its hydrodynamic
limit as $N\to\infty$, in the diffusive space-time scaling, when the initial
density profile is supercritical. More precisely, the macroscopic density of
particles evolves in the bulk according to a fast diffusion equation as in the
periodic case, and besides, we show that the boundary-driven FEP exhibits a
very peculiar behaviour: unlike for the classical SSEP, and due to the
two-phased nature of the FEP, the reservoirs impose Dirichlet boundary
conditions which do not coincide with their equilibrium densities. The proof is
based on the classical entropy method, but requires significant adaptations to
account for the FEP's non-product stationary states and to deal with the
non-equilibrium setting.
