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Research Article | Open Access

A symmetry theorem in two-phase heat conductors

Hyeonbae Kang1, Shigeru Sakaguchi2( )
Department of Mathematics and Institute of Applied Mathematics, Inha University, Incheon 22212, S. Korea
Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan
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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 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 , α , 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.

Keywords

heat diffusion equationtwo-phase heat conductorsCauchy problemstationary isothermic surfacemethod of moving planestransmission conditions

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Mathematics in Engineering
Volume 5 Issue 3,
June 2023
Pages 1-7
DOI: 10.3934/mine.2023061

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Cite this article:
Kang H, Sakaguchi S. A symmetry theorem in two-phase heat conductors. Mathematics in Engineering, 2023, 5(3): 1-7. https://doi.org/10.3934/mine.2023061

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Received: 26 October 2022
Revised: 16 November 2022
Accepted: 16 November 2022
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)