The porosity of a compacting sedimentary basin satisfies a nonlinear pseudo-parabolic partial differential equation. This equation is distinguished from the classical porous medium equation by a third order term, a degenerate elliptic operator in spatial variables acting on the time derivative of the solution. We describe the derivation of the model equation, review classical results for pseudo-parabolic equations and their relation to parabolic equations, present new existence and regularity results for this nonlinear PDE, and show they are consistent with expected behavior of solutions in this context.