Convexity breaking of the free boundary for porous medium equations

Kazuhiro Ishige, Paolo Salani

Research output: Contribution to journalArticle

9 Citations (Scopus)

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

Original languageEnglish
Pages (from-to)75-84
Number of pages10
JournalInterfaces and Free Boundaries
Volume12
Issue number1
DOIs
Publication statusPublished - 2010 Aug 4

ASJC Scopus subject areas

  • Surfaces and Interfaces

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