双相热导体中超平面的特征u

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2024-07-26 DOI:10.4310/cag.2023.v31.n7.a9

Cavallina,Lorenzo, Sakaguchi,Shigeru, Udagawa,Seiichi

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引用次数: 0

摘要

我们考虑在整个欧几里得空间中的热扩散方程的考奇问题，该空间由两种具有不同恒定传导性的介质组成，其中一种介质的初始温度为 0，另一种介质的初始温度为 1。假设界面是连通的，且均匀属于 $C^{6}$。我们将证明，如果界面具有时变恒温，那么它一定是一个超平面。

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A characterization of a hyperplane in two-phase heat conductorsu

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.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.