Self-similar focusing in porous media: An explicit calculation
D. G. Aronson · Discrete and Continuous Dynamical Systems - B · 2012
We consider a porous medium flow in which the material isinitially distributed in the exterior of an empty region (a hole) and studythe final stage of the hole-filling process as well as the initial stage ofthe post filling regime. It is known that in axially symmetric flow thehole-filling is asymptotically described by a self-similar solution whichdepends on a constant determined by the initial distribution. The postfilling accumulation process is also locally described by a self-similarsolution which in turn is characterized by a constant. In general, theseconstants must be found either experimentally or numerically. Here wepresent an example of a one-dimensional flow where the constants areobtained explicitly.