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Communications in Analysis and Geometry
Volume 31 (2023)
Number 7
A characterization of a hyperplane in two-phase heat conductors
Pages: 1867 – 1888
DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n7.a9
Authors
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 connected and uniformly of class $C^6$. We show that if the interface has a time-invariant constant temperature, then it must be a hyperplane.
This research was partially supported by the Grants-in-Aid for Scientific Research (B) (#18H01126 and #17H02847) and JSPS Fellows (#18J11430) of Japan Society for the Promotion of Science.
Received 31 December 2019
Accepted 14 October 2020
Published 10 August 2024