Geodesic
Convexity breaking of the free boundary for porous medium equations
Kazuhiro Ishige1 ; Paolo Salani2
1Tohoku University, Sendai, Japan
2Università degli Studi di Firenze, Italy
Interfaces and free boundaries, Tome 12 (2010) no. 1, pp. 75-84

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DOI

We investigate the preservation of convexity of the free boundary by the solutions of the porous medium equation. We prove that starting with an initial datum with some kind of suboptimal αconcavity property, the convexity of the positivity set can be lost in a short time.
DOI : 10.4171/ifb/227
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Kazuhiro Ishige  1   ; Paolo Salani  2

1 Tohoku University, Sendai, Japan
2 Università degli Studi di Firenze, Italy 
Kazuhiro Ishige; Paolo Salani. Convexity breaking of the free boundary for porous medium equations. Interfaces and free boundaries, Tome 12 (2010) no. 1, pp. 75-84. doi: 10.4171/ifb/227
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     number = {1},
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