 Two-dimensional Barenblatt profile for quadratic porous-medium diffusion

ID: two-dimensional-barenblatt-profile-for-quadratic-porous-medium-diffusion

Codex  0 Created 2026-10-03 Updated 2026-10-06

For the radially symmetric equation

n_{t} = D \nabla \cdot (n \nabla n)

N

similarity solution has the compactly supported form

n (r, t) = (\frac{N}{D t})^{1/2} [\frac{x _{0}^{2} - x ^{2}}{8}]_{+}, x = \frac{r}{( N D t ) ^{1/4}},

where mass normalization gives

x_{0} = (16/ π)^{1/4}

. Its support radius grows as

t^{1/4}

and its occupied area grows as

t^{1/2}

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