Open AccessAsymptotic analysis for the electric field concentration with geometry of the core-shell structure
Author(s) -
Zhiwen Zhao
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2022012
Subject(s) - mathematics , geometry , boundary (topology) , matrix (chemical analysis) , type (biology) , field (mathematics) , combinatorics , mathematical analysis , pure mathematics , materials science , composite material , ecology , biology
In the perfect conductivity problem arising from composites, the electric field may become arbitrarily large as \begin{document}$ \varepsilon $\end{document} , the distance between the inclusions and the matrix boundary, tends to zero. In this paper, by making clear the singular role of the blow-up factor \begin{document}$ Q[\varphi] $\end{document} introduced in [ 27 ] for some special boundary data of even function type with \begin{document}$ k $\end{document} -order growth, we prove the optimality of the blow-up rate in the presence of \begin{document}$ m $\end{document} -convex inclusions close to touching the matrix boundary in all dimensions. Finally, we give closer analysis in terms of the singular behavior of the concentrated field for eccentric and concentric core-shell geometries with circular and spherical boundaries from the practical application angle.