Rate of Convergence to Barenblatt Profiles for the Fast Diffusion   Equation
  We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data. 
Marek Fila, Juan Luis Vazquez, Michael Winkler and Eiji Yanagida
math.AP