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arXiv · 1910.06757

A characterization of a hyperplane in two-phase heat conductors

Lorenzo Cavallina·Shigeru Sakaguchi·Seiichi Udagawa
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Abstract

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has temperature 0 and the other has temperature 1. Suppose that the interface is uniformly of class $C^6$. We show that if the interface has a time-invariant constant temperature, then it must be a hyperplane.

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Lorenzo Cavallina, Shigeru Sakaguchi, Seiichi Udagawa. 2019-10-12. A characterization of a hyperplane in two-phase heat conductors. https://arxiv.org/abs/1910.06757

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