Electromagnetic model of a hidden object (Q627741)

This note is a short description of the homogenization to the elliptic equation \(\nabla\cdot(\nabla u /\mu)+\omega^2\varepsilon u=0\), which models a plane wave propagation in a non homogeneous multiply connected domain. The non homogeneity of the medium is of a periodic type. The macroscopic permittivity \(\varepsilon\) and permeability \(\mu\) depend on the microscopic structure. The initial problem is replaced by a transmission problem and next by a system of integral equations.