= Radial cubic-diffusion source profile
{title2=$F(\xi)=\sqrt{[1-\xi^2]_+}$}
For the planar <porous medium equation> $n_t=[D_0/(3n_0^2)]\Delta(n^3)$, the mass-$Q$ point-source <similarity solution> is $n=n_0\lambda^{-2}\sqrt{[1-r^2/(r_0^2\lambda^2)]_+}$, with $\lambda=(6D_0t/r_0^2)^{1/6}$ and $r_0^2=3Q/(2\pi n_0)$. Its front grows as $t^{1/6}$ and its central density falls as $t^{-1/3}$. The <mass conservation> integral uses the planar area element $2\pi r\,dr$. Although the density slope diverges at the front, its diffusion flux vanishes there, giving a compactly supported <weak solution> with initial measure $Q\delta^{(2)}$.
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