Title: Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps,
Abstract: We consider an exclusion process with long jumps in the box $\Lambda\_N=\{1,
\ldots,N-1\}$, for $N \ge 2$, in contact with infinitely extended reservoirs on
its left and on its right. The jump rate is described by a transition
probability $p(\cdot)$ which is symmetric, with infinite support but with
finite variance. The reservoirs add or remove particles with rate proportional
to $\kappa N^{-\theta}$, where $\kappa>0$ and $\theta \in\mathbb R$. If
$\theta>0$ (resp. $\theta<0$) the reservoirs add and fastly remove (resp.
slowly remove) particles in the bulk. According to the value of $\theta$ we
prove that the time evolution of the spatial density of particles is described
by some reaction-diffusion equations with various boundary conditions.