  An interacting particle system made of diffusion processes with local
interaction is considered and the macroscopic limit to a nonlinear PDE is
investigated. Few rigorous results exists on this problem and in particular the
explicit form of the nonlinearity is not known. The paper reviews this subject,
some of the main ideas to get the limit nonlinear PDE and provides both
heuristic and numerical informations on the precise form of the nonlinearity
which are new with respect to the literature and coherent with the few known
informations.
