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 concavity property, the convexity of the positivity set can be lost in a short time.

Convexity breaking of the free boundary for porous medium equations / K. Ishige; P. Salani. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - STAMPA. - 12 issue 1:(2010), pp. 75-84. [10.4171/IFB/227]

Convexity breaking of the free boundary for porous medium equations

SALANI, PAOLO
2010

Abstract

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 concavity property, the convexity of the positivity set can be lost in a short time.
2010
12 issue 1
75
84
K. Ishige; P. Salani
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/371276
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