  We analyze the hydrodynamic behavior of the porous medium model in a discrete
space $\{0,\ldots, n\}$, where the sites $0$ and $n$ stand for reservoirs. Our
strategy relies on the entropy method of Guo, Papanicolau and Varadhan.
However, this method cannot be straightforwardly applied, since there are
configurations that do not evolve according to the dynamics (blocked
configurations). In order to avoid this problem, we slightly perturbed the
dynamics in such a way that the macroscopic behavior of the system keeps
following the porous medium equation, but with boundary conditions which depend
on the reservoirs strength's.
