Off-equilibrium dynamics in a singular diffusion model

We introduce a schematic nonlinear diffusion model where density fluctuatio ns induce a rich out of-equilibrium dynamics. The properties of the model a re studied by numerical simulations and analytically in a mean field approx imation. At low temperatures and high densities we find a long off-equilibr ium glassy region, where the system evolves out of an initially pinned stat e showing aging and a slow decay of the autocorrelation as an enhanced powe r law, along with strong spatial heterogeneities and violation of the fluct uation-dissipation theorem.