consisting of concentric spherical shells. Their main emphasis was to check the MF description of the stable and metastable states rather than to study the dynamics of the phase transition itself. Cerruti-Sola, Cipriani, and Pettini [@pet] studied the phase diagram of a more realistic 3-dimensional particle system by using Monte Carlo and MD methods. Their studies again focused on the equilibrium properties of the system rather than on the dynamics of the transitions. In addition, their general conclusions about the second order of the gravitational phase transition apparently contradict the MF results [@ki2; @usg; @dv; @chi].

Here, we attempt to resolve this contradiction. A MF description of the dynamics of collapse in ensembles of self-gravitating Brownian particles with a bare $1/r$ interaction based on a Smoluchowski equation was developed by Chavanis et al [@chs]. It predicts a self-similar evolution of the central part of density distribution to a finite-time singularity. However, the precise nature of the random force and friction terms in the corresponding Fokker-Plank equation as well as the applicability of the overdamped limit used to reduce the Fokker-Plank equation to the Smoluchowski equation are not entirely understood. A more rigorous approach based on the Fokker-Plank equation with Landau 