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On some local property of the shape of interfaces for the porous media equation
Author(s) -
Hayasida Kazuya
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610765
Subject(s) - porous medium , mathematics , property (philosophy) , regular polygon , cauchy distribution , absorption (acoustics) , porosity , mathematical analysis , geometry , materials science , composite material , philosophy , epistemology
We consider the porous media equation with absorption for various conditions and prove that the shape of ist interface never becomes strongly upward convex. For this sake we derive an improperly posed estimate for solutions of the porous media equation for the non‐characteristic Cauchy problem (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)