A Continuum of Extinction Rates for the Fast Diffusion Equation

We find a continuum of extinction rates for solutions $u(y,τ)\ge 0$ of the fast diffusion equation $u_τ=Δu^m$ in a subrange of exponents $m\in (0,1)$. The equation is posed in $\ren$ for times up to the extinction time $T>0$. The rates take the form $\|u(\cdot,τ)\|_\infty\sim (T-τ)^θ$ \ for a whole interval of $θ>0$. These extinction rates depend explicitly on the spatial decay rates of initial data.

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