接地凸形导体中热点的位置
The location of the hot spot in a grounded convex conductor
摘要：
本文研究了具有幺正初始温度和零温度接地边界的凸形热导体中（唯一）热点的位置。我们提出了两种方法来定位的热点：前者是基于有关的想法Alexandrov-Bakelmann-Pucci最大值原理和蒙日-安培方程;后者依赖于Alexandrov的反射原理。然后，我们展示了如何这样的问题可以简化的情况下，导体是一个多面体。最后，我们给出了一些数值计算。
英文摘要：
We investigate the location of the (unique) hot spot in a convex heat conductor with unitary initial temperature and with boundary grounded at zero temperature. We present two methods to locate the hot spot: the former is based on ideas related to the Alexandrov-Bakelmann-Pucci maximum principle and Monge-Ampère equations; the latter relies on Alexandrov's reflection principle. We then show how such a problem can be simplified in case the conductor is a polyhedron. Finally, we present some numerical computations.
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