A symmetry theorem in two-phase heat conductors

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-27 DOI:10.3934/mine.2023061

Hyeonbae Kang, Shigeru Sakaguchi

引用次数: 0

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, \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.

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两相热导体中的一个对称定理

我们考虑由两个具有不同恒定电导率的介质组成的整个欧几里得空间中的热扩散方程的柯西问题，其中一个介质的初始温度为0，另一个介质温度为1。在假设一个介质是有界的，并且界面是$C^｛2，\alpha｝$类的情况下，我们证明了如果界面是静止等温的，那么它一定是一个球体。直接利用Serrin引起的平面移动方法来证明结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.