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Interfaces with a corner point in one‐dimensional porous medium flow
Author(s) -
Aronson D. G.,
Caffarelli L. A.,
Vazquez J. L.
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380404
Subject(s) - smoothness , porous medium , mathematics , flow (mathematics) , point (geometry) , initial value problem , porosity , class (philosophy) , mathematical analysis , mechanics , calculus (dental) , geometry , computer science , geology , physics , geotechnical engineering , medicine , dentistry , artificial intelligence
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.