两相热导体温度的大时间行为
Large time behavior of temperature in two-phase heat conductors
摘要：
考虑由两种不同的常电导率介质组成的整个欧几里得空间中热扩散方程的Cauchy问题。当初始温度在一种介质上为0，在另一种介质上为$1$时，研究了温度的大时间行为，即问题的解。我们表明，在一定的几何条件下的配置的介质，温度是稳定的常数，时间趋于无穷大。我们还表明，温度一般振荡，是不稳定的例子。
英文摘要：
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities. The large time behavior of temperature, the solution of the problem, is studied when initially temperature is assigned to be 0 on one medium and $1$ on the other. We show that under a certain geometric condition of the configuration of the media, temperature is stabilized to a constant as time tends to infinity. We also show by examples that temperature in general oscillates and is not stabilized.
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