复杂介质中的传热
Heat transfer in a complex medium
摘要：
热方程被认为是在复杂的介质中由许多小物体（颗粒）嵌入在一个给定的材料。在小物体的表面上施加阻抗边界条件。当小天体的特征尺寸$a$趋于零时，它们的总数$\mathcal{N}(a)$以适当的速率趋于无穷大，相邻小天体之间的距离$d = d(a)$趋于零时，导出了极限场的方程：$a << d$，$\lim_{a\to 0}\frac{a}{d(a)}=0$ .小天体的分布没有周期性。这些结果是基本的方法，创建一个介质中，热信号沿给定的线传输。这种方法的技术部分是基于一个反问题，找到潜在的规定的特征值。
英文摘要：
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting field is derived when the characteristic size $a$ of the small bodies tends to zero, their total number $\mathcal{N}(a)$ tends to infinity at a suitable rate, and the distance $d = d(a)$ between neighboring small bodies tends to zero: $a << d$, $\lim_{a\to 0}\frac{a}{d(a)}=0$. No periodicity is assumed about the distribution of the small bodies. These results are basic for a method of creating a medium in which heat signals are transmitted along a given line. The technical part for this method is based on an inverse problem of finding potential with prescribed eigenvalues.
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