Fowler–Yang equations

${\displaystyle {\frac {\partial \phi }{\partial t}}={\frac {\partial }{\partial z}}[(1-\phi )u],}$
${\displaystyle u=\lambda \phi ^{m}\left[{\frac {\partial ^{2}u}{\partial z^{2}}}-(1-\phi )\right],}$
where u is the Darcy velocity and ${\displaystyle \phi }$ is the porosity of the porous media. In addition, 0 < λ < 105 is a constant, and while m = 8. This system is highly nonlinear, which can explain the transition from one behaviour to another in pressure solution.