How an Initially Stationary Interface Begins to Move in Porous Medium Flow
D. G. Aronson, Luis A. Caffarelli, Shoshana Kamin · SIAM Journal on Mathematical Analysis · 1983
The interface we study is the boundary of the support of the density of a gas flowing in a homogeneous porous medium. It is known that for certain initial distributions the interface remains stationary for a positive time. We derive upper and lower estimates for this waiting time and give a condition which is sufficient to guarantee that the interface begins to move in a smooth manner. In some cases our estimates give the exact waiting time.