English

The Stefan problem and concavity

Analysis of PDEs 2021-11-17 v1

Abstract

We construct examples for the one-phase Stefan problem which show that α\alpha-concavity of the solution is in general not preserved in time, for 0α<1/20 \le \alpha <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.

Keywords

Cite

@article{arxiv.2004.04284,
  title  = {The Stefan problem and concavity},
  author = {Albert Chau and Ben Weinkove},
  journal= {arXiv preprint arXiv:2004.04284},
  year   = {2021}
}

Comments

12 pages

R2 v1 2026-06-23T14:44:56.354Z