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A continuum of extinction rates for the fast diffusion equation

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  • We find a continuum of extinction rates for solutions $u(y,\tau)\ge 0$ of the fast diffusion equation $u_\tau=\Delta u^m$ in a subrange of exponents $m\in (0,1)$. The equation is posed in $R^n$ for times up to the extinction time $T>0$. The rates take the form $\|u(\cdot,\tau)\|_\infty$ ~ $(T-\tau)^\theta$ for a whole interval of $\theta>0$. These extinction rates depend explicitly on the spatial decay rates of initial data.
    Mathematics Subject Classification: Primary: 35K65; Secondary: 35B40.

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