  We study the long-time asymptotics of a certain class of nonlinear diffusion
equations with time-dependent diffusion coefficients which arise, for instance,
in the study of transport by randomly fluctuating velocity fields. Our primary
goal is to understand the interplay between anomalous diffusion and
nonlinearity in determining the long-time behavior of solutions. The analysis
employs the renormalization group method to establish the self-similarity and
to uncover universality in the way solutions decay to zero.
