Asymptotic analysis of an array of closely spaced absolutely conductive inclusions
Leonid V. Berlyand, Giuseppe Cardone, Yuliya Gorb, Gregory P. Panasenko · Networks and Heterogeneous Media · 2006
We consider the conductivity problem in an array structure withsquare closely spaced absolutely conductive inclusions of the highconcentration, i.e. the concentration of inclusions is assumed tobe close to 1. The problem depends on two small parameters:$\varepsilon$, the ratio of the period of the micro-structure tothe characteristic macroscopic size, and $\delta$, the ratio ofthe thickness of the strips of the array structure and the periodof the micro-structure. The complete asymptotic expansion of thesolution to problem is constructed and justified as both$\varepsilon$ and $\delta$ tend to zero. This asymptotic expansionis uniform with respect to $\varepsilon$ and $\delta$ in the area$\{\varepsilon=O(\delta^{\alpha}),~\delta=O(\varepsilon^{\beta})\}$ for any positive $\alpha, \beta.$