论文标题
来自边界数据的一个奇怪的术语
A strange term coming from the boundary data
论文作者
论文摘要
在本文中，我在穿孔的域中得出了泊松方程的局限性行为，但要遵守不均匀的罗宾边界条件。在本文的上半年，我得出了非周期性域和任意边界数据的广义限制。在本文的后半部分，我证明，对于定期布置的球体和每个球体上相同的罗宾边界数据，Poisson方程的均质极限满足了helmholtz方程，并在域数据中具有附加项，这代表了不均匀的Robin边界数据的贡献。这些结果是对Kaizu的工作的概括，后者衍生了解决方案的均质罗宾问题的极限。
In this paper, I derive the limiting behaviour of the solutions to Poisson's equation, in a perforated domain, subject to inhomogeneous Robin boundary conditions. In the first half of the paper, I derive a generalised limit for non-periodic domains and arbitrary boundary data. In the second half of this paper, I demonstrate that for periodically arranged spheres and identical Robin boundary data on each sphere, the homogenised limit of Poisson's equation satisfies the Helmholtz equation with an additional term in the domain data, which represents the contribution from the inhomogeneous Robin boundary data. These results are a generalisation of the work of Kaizu, who derived the limit of the solutions to the homogeneous Robin problem.
