We show the validity of the interface equation which describes the behavior of the support of the solution to the one-dimensional porous media equation with absorption. Our proof is based on the finite difference methods.
Tatsuyuki Nakaki. Kenji Tomoeda. "A finite difference approach to the interface equation for some nonlinear diffusion equations with absorption." Proc. Japan Acad. Ser. A Math. Sci. 77 (2) 32 - 37, Feb. 2001. https://doi.org/10.3792/pjaa.77.32