Hydrodynamical behavior for the generalized symmetric exclusion with open boundary

We analyze the generalized symmetric exclusion process, which allows at most $\alpha$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $\theta \in \mathbb{R}$. We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of $\theta$, the equation is supplemented with different boundary conditions. Setting $\alpha =1$ we find the results known in [1] for the symmetric simple exclusion process.