  We consider the symmetric simple exclusion process in the interval
$\La_N:=[-N,N]\cap\mathbb Z$ with births and deaths taking place respectively
on suitable boundary intervals $I_+$ and $I_-$, as introduced in De Masi et al.
(J. Stat. Phys. 2011). We study the stationary measure density profile in the
limit $N\to\infty$
