A symmetry theorem in two-phase heat conductors

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 medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface...

Full description

Bibliographic Details
Main Authors: Hyeonbae Kang, Shigeru Sakaguchi
Format: Article
Language:English
Published: AIMS Press 2023-09-01
Series:Mathematics in Engineering
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/mine.2023061?viewType=HTML
Description
Summary: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 medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface is of class $ C^{2, \alpha} $, we show that if the interface is stationary isothermic, then it must be a sphere. The method of moving planes due to Serrin is directly utilized to prove the result.
ISSN:2640-3501