Porous medium equation

Summary

The porous medium equation is the nonlinear diffusion equation $u_t = \Delta(u^m)$ with $m > 1$. It models the flow of a gas through a porous rock, among other things. The diffusion coefficient $m u^{m-1}$ vanishes where $u = 0$, so the equation is degenerate there. As a consequence, disturbances travel with finite speed and solutions can have compact support with a moving free boundary.