Barenblatt solution
= Barenblatt solution
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The Barenblatt solution is a mass-preserving <similarity solution> of the <porous medium equation>. For $u_t=\beta(uu_x)_x$ in one dimension it has the form
$$
u(x,t)=\left[A t^{-1/3}-\frac{x^2}{6\beta t}\right]_+.
$$