两相热导体中的一个对称定理

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Mathematics in Engineering Pub Date : 2022-10-27 DOI:10.3934/mine.2023061

Hyeonbae Kang, Shigeru Sakaguchi

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引用次数: 0

摘要

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。

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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 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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