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Interfaces with a corner point in one-dimensional porous medium flow. (English) Zbl 0544.35058
We prove that for a large class of initial distributions the solution 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 \(x\to 0\). We also give sufficient conditions for the smoothness of the interface which improve previous results.

MSC:
35K55 Nonlinear parabolic equations
76S05 Flows in porous media; filtration; seepage
35B65 Smoothness and regularity of solutions to PDEs
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