We consider a family of exclusion processes defined on the discrete interval with weak boundary interaction that allows the creation and annihilation of particles on a neighborhood of radius L of the boundary under very general rates. We prove that the hydrodynamic equation is the heat equation with non-linear Robin boundary conditions. We present a particular choice of boundary rates for which we have multiple stationary solutions but for which it still holds the uniqueness of the solution of its hydrodynamic equation. We also prove the associated dynamical large deviations principle. Joint work with Claudio LandimĀ andĀ Beatriz Salvador.