Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Kang, Hyeonbae¹  Yun, KiHyun² 

[1] Inha Univ, Dept Math, Incheon 22212, South Korea

[2] Hankuk Univ Foreign Studies, Dept Math, Yongin 17035, Gyeonggi Do, South Korea

关键词: Field enhancement;    Gradient blow-up;    Bow-tie structure;    Corner singularity;    High contrast;    Perfect conductor;   

DOI  :  10.1016/j.jde.2018.10.018

来源: Elsevier

【 摘 要 】

This paper deals with the field enhancement due to insertion of a bow-tie structure of perfectly conducting inclusions into the two-dimensional space with a given field. The field enhancement is represented by the gradient blow-up of a solution to the conductivity problem. The bow-tie structure consists of two disjoint bounded domains which have corners with possibly different aperture angles. The domains are parts of cones near the vertices which are nearly touching to each other. We construct functions explicitly which characterize the field enhancement. As consequences, we derive optimal estimates of the gradient in terms of the distance between two inclusions and aperture angles of the corners. The estimates show in quantitatively precise way that the field is enhanced beyond the corner singularities due to the interaction between two inclusions, and the blow-up rate is much higher than the one for the case of inclusions with smooth boundaries. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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