The Stefan problem and concavity
Abstract
We construct examples for the one-phase Stefan problem which show that $\alpha$-concavity of the solution is in general not preserved in time, for $0 \le \alpha <1/2$. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.04284
- arXiv:
- arXiv:2004.04284
- Bibcode:
- 2020arXiv200404284C
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 12 pages