Interfaces with a corner point in one‐dimensional porous medium flow
D. G. Aronson, Luis A. Caffarelli, J. L. Vazquez · Communications on Pure and Applied Mathematics · 1985
Abstract We prove that for a large class of initial distributions the solutions of the initial value problem for the one‐dimensional porous medium equation have interfaces which start to move abruptly after a positive waiting time. This happens, for example, if the initial pressure is o (|x| 2 ) as x → 0. We also give sufficient conditions for the smoothness of the interface which improve previous results.