The family of fast diffusions, ut = [u-ux]x where  was between 0 and 2, was considered. It was pointed out that, when  was between 1 and 2, fast diffusion coexisted with super-fast processes. Up to termination within a finite time, these equations were of time-space separable form. The remarkable properties of ut[ln(u)]xx were found to govern the understanding of these processes. Thus, 2 interacting kinks led to a super-fast shrinking pattern or to the continued motion of 2 poles. When  was equal to unity, super-fast axisymmetrical diffusion coexisted with modified fundamental diffusion: a response to a singular core, and a ring of  sources. In the case of 3 dimensions, the fast ( between 0 and 2/3) and separable ( between 4/5 and 1) super-fast processes were distinct. Inhomogeneity of the medium was also considered.

P.Rosenau: Physical Review Letters, 1995, 74[7], 1056-9