The Stefan problem and concavity

Albert Chau, Ben Weinkove*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We construct examples for the one-phase Stefan problem which show that α-concavity of the solution is in general not preserved in time, for 0 ≤ α< 1 / 2. In particular, this shows that, in contrast to the case of the heat equation for a fixed convex domain, log concavity is not preserved for solutions of the Stefan problem.

Original languageEnglish (US)
Article number176
JournalCalculus of Variations and Partial Differential Equations
Volume60
Issue number5
DOIs
StatePublished - Oct 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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