Exact solutions for the insulated and perfect conductivity problems with concentric balls

被引：0
作者：
Zhao, Zhiwen [1 ]
机构：
[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China
来源：
MATHEMATICS IN ENGINEERING | 2023年 / 5卷 / 03期
关键词：
exact solutions; the insulated and perfect conductivity problems; concentric balls; the electric field; high-contrast composites; blow-up; ELECTRIC-FIELDS; BLOW-UP;
D O I：
10.3934/mine.2023060
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The insulated and perfect conductivity problems arising from high-contrast composite materials are considered in all dimensions. The solution and its gradient, respectively, represent the electric potential and field. The novelty of this paper lies in finding exact solutions for the insulated and perfect conductivity problems with concentric balls. Our results show that there appears no electric field concentration for the insulated conductivity problem, while the electric field for the perfect conductivity problem exhibits sharp singularity with respect to the small distance between interfacial boundaries of the interior and exterior balls. This discrepancy reveals that concentric balls is the optimal structure of insulated composites, but not for superconducting composites.
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页码：1 / 11
页数：11
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