  We study the stationary non-local equation which corresponds to the energy
functional of a one-dimensional Ising spin system, in which particles interact
via a Kac potential. The boundary conditions share the same sign and both lie
above the value $m^*\left(\beta\right)=\sqrt{1-1/\beta}$, which divides the
metastable region from the unstable one, the inverse temperature being fixed
and larger than the critical value $\beta_c=1$. Due to the non-equilibrium
setting, a non zero magnetization current, which scales with the inverse of the
size of the volume $\varepsilon^{-1}$, do flow in the system. Here
$\varepsilon^{-1}$ also represents the ratio of macroscopic and mesoscopic
length. We show that for $\varepsilon>0$ small enough, the stationary profile
has no discontinuities so that no phase transition occurs; although expected
when the magnetizations are larger than $m_{\beta}$, this turns out to be non
trivial at all in the metastable region. Moreover, when
$\varepsilon^{-1}\to\infty$, the solution converges to that of the
corresponding macroscopic problem, i.e. the local diffusion equation. The
validity of the Fick's law in this context is then established.
