Porous medium equation (source code)

= Porous medium equation
{title2=$u_t=\Delta(u^m)$}
{wiki}

The porous medium equation $u_t=\Delta(u^m)$ with $m>1$ is a <nonlinear partial differential equation> whose diffusivity vanishes at $u=0$. Unlike the <heat equation>, it has compactly supported solutions with finite propagation speed.