= Spherical nonlinear-diffusion source profile
{title2=$r_0=(75Mkt)^{1/5}$}
For $C_t=k\nabla\cdot(C\nabla C)$ in three dimensions and total mass $4\pi M$, the nonnegative radial source solution is $C=M^{2/5}(kt)^{-3/5}f(r/(Mkt)^{1/5})$, with $f(\xi)=(75^{2/5}-\xi^2)_+/10$. Integrating the similarity equation once gives $ff'=-\xi f/5$, and normalization $\int_0^\infty\xi^2f\,d\xi=1$ fixes the compact-support radius. The flux vanishes at the moving front, so the profile solves the equation weakly and approaches the prescribed point mass as time tends to zero.
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