论文标题
完美电导率问题中电场浓度的渐近学
Asymptotics for the electric field concentration in the perfect conductivity problem
论文作者
论文摘要
在复合材料的完美导电性问题中，电场在两个夹杂物之间的狭窄区域集中在狭窄的区域中，并且当夹杂物之间的距离趋于零时，始终会变得任意大。为了表征这种奇异行为，我们捕获了梯度的前学期，并揭示了爆炸速率取决于它们两个相邻夹杂物的相对凸度。另一方面，发现一个线性数据的爆炸因子可以确定爆炸是否发生。
In the perfect conductivity problem of composite material, the electric field concentrates in a narrow region in between two inclusions and always becomes arbitrarily large when the distance between inclusions tends to zero. To characterize such singular behavior, we capture the leading term of the gradient and reveal that the blow-up rates are determined by their relative convexity of the two adjacent inclusions. On the other hand, a blow-up factor, which is a linear functional of boundary data, is found to determine the blow-up will occur or not.
