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.
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