I will present some results of a paper by Igbida (https://arxiv.org/abs/2105.00182) where the author studies the incompressible Hele-Shaw problem, a well-known PDE system which can be applied to biology models (e.g. tissue growth) and crowd motion. The density evolves under a given linear drift, a source term and is subject to a hard congestion effect through a density constraint. I will show how to obtain an L1-contraction principle for the problem set in a bounded domain under mixed boundary conditions. The method combines DiPerna-Lions' renormalized formulation and Kruzhkov's doubling and de-doubling technique. This result implies, in particular, a new uniqueness result that holds under mild assumptions on the prescribed velocity field.