On the asymptotic behaviour of Spitzer's model for evolution of one-dimensional point systems

A nearest-neighbor gradient dynamics of one-dimensional infinite particle systems is considered; the model admits a two-parameter family of stationary configurations. Some domains of attraction of stationary configurations are described, and the continuum (hydrodynamical) limit of the system is investigated. It is shown that the mean density of points satisfies a nonlinear diffusion equation in the hydrodynamical limit.Research supported by I.H.E.S., Bures-sur-Yvette, France.