Slow growth of solutions of super-fast diffusion equations with   unbounded initial data
  We study positive solutions of the super-fast diffusion equation in the whole space with initial data which are unbounded as $|x|\to\infty$. We find an explicit dependence of the slow temporal growth rate of solutions on the initial spatial growth rate. A new class of self-similar solutions plays a significant role in our analysis. 
Marek Fila and Michael Winkler
math.AP