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Some characterizations of parallel hyperplanes in multi-layered heat conductors
Journal de Mathématiques Pures et Appliquées ( IF 2.3 ) Pub Date : 2020-06-22 , DOI: 10.1016/j.matpur.2020.06.007
Shigeru Sakaguchi

We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has temperature 1. Under some appropriate conditions, it is shown that, if either the interface between the lower layer and the middle layer is a stationary isothermic surface or there is a stationary isothermic surface in the middle layer near the lower layer, then the two interfaces must be parallel hyperplanes. Similar propositions hold true, either if a stationary isothermic surface is replaced by a surface with the constant flow property or if the Cauchy problem is replaced by an appropriate initial-boundary value problem.



中文翻译:

多层热导体中平行超平面的一些特征

我们考虑了由三层具有恒定电导率的三层组成的整个空间中的热扩散方程的柯西问题,其中上层和中层最初的温度为0,下层的温度为1。 ,如果下层和中间层之间的界面是固定的等温表面,或者在靠近下层的中间层中有固定的等温表面,则两个界面必须是平行的超平面。无论是将固定的等温曲面替换为具有恒定流动特性的曲面,还是将柯西问题替换为适当的初始边界值问题,类似的主张都成立。

更新日期:2020-06-22
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