= Planar volume-conserving nonlinear-diffusion similarity
{title2=$h_t=A(h^nh_x)_x$}
For $n,A>0$, the one-dimensional <porous medium equation> $h_t=A(h^nh_x)_x$ has a volume-preserving <similarity solution> $h=[c_n(R^2-x^2)/(At)]_+^{1/n}$, where $c_n=n/[2(n+2)]$ and $R\propto t^{1/(n+2)}$. On a reflecting half-line with conserved area $M$, $R=[M(At/c_n)^{1/n}/I_n]^{n/(n+2)}$, where $I_n=\tfrac12 B(\tfrac12,1+1/n)$. For a whole symmetric release use half its total area as $M$. The <Beta function> fixes normalization, while finite-front zero <volume flux> fixes the edge condition.
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