Special asymptotics for a critical fast diffusion equation

Abstract

We find a continuum of extinction rates of solutions of the Cauchy problem forthe fast diffusion equation$u_\tau=\nabla\cdot(u^{m-1}\,\nabla u)$ with $m=m_*:=(n-4)/(n-2)$, here $n>2$ is the space-dimension. The extinction ratesdepend explicitly on thespatial decay rates of initial data and contain a logarithmic term.