Scaling limit for a mechanical system of interacting particles

A system of a large number of classical particles moving on a onedimensional segment with virtually reflecting boundaries is studied. The particles interact with one another through repulsive pair-potential forces and are subjected to resistance proportional to their velocities. Because of the latter it is only the number of particles that is conserved under the evolution of the system. It is proved that in the hydrodynamic limit of diffusion type scaling the normalized counting measure of particle locations converges and its limiting density is governed by a non-linear diffusion equation which in typical cases is of porous media equation type.