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arXiv · 2004.04284

The Stefan problem and concavity

Albert Chau·Ben Weinkove
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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.

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Albert Chau, Ben Weinkove. 2020-04-08. The Stefan problem and concavity. https://arxiv.org/abs/2004.04284

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