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Two-dimensional Barenblatt solution with diffusivity proportional to concentration

For

C_{t} = k \nabla \cdot (C \nabla C)

with total mass

2 π M

,

C (r, t) = \frac{M}{k t} (\frac{1}{2} - \frac{1}{8} \frac{r ^{2}}{M k t})_{+} .

Its compact support has radius

r_{0} (t) = (32 M k t)^{1/4}

.

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- Linear-reaction time change for quadratic nonlinear diffusion Two-dimensional Barenblatt solution with diffusivity proportional to concentration 16

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