A Continuum of Extinction Rates for the Fast Diffusion Equation

We find a continuum of extinction rates for solutions $u(y,\tau )\ge 0$ of the fast diffusion equation $u_{\tau }=\mathrm{\Delta }{u}^m$ in a subrange of exponents $m\in (0,1)$\mathrm{.}Theequationisposedin$\ren$fortimesuptotheextinctiontime$T>0$\mathrm{.}Theratestaketheform$|u(\cdot,\tau)|_\infty\sim (T-\tau)^\theta$
for a whole interval of $\theta >0$. These extinction rates depend explicitly on the spatial decay rates of initial data.