Two-dimensional Barenblatt profile for quadratic porous-medium diffusion

For the radially symmetric equationin two dimensions, the mass-$N$ similarity solution has the compactly supported formwhere mass normalization gives $x_0=(16/\pi {)}^{1/4}$. Its support radius grows as $t^{1/4}$ and its occupied area grows as $t^{1/2}$.