A characterization of a hyperplane in two-phase heat conductors
Lorenzo Cavallina, Shigeru Sakaguchi, Seiichi Udagawa · arXiv (Cornell University) · 2019
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.