Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator

Micol Amar, Daniele Andreucci, Roberto Gianni, Claudia Timofte

Published 2020-01-21Version 1

We study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the composite. This leads to the appearance of a peculiar displacement current governed by a Laplace-Beltrami pseudo-parabolic equation. This pseudo-parabolic character is present also in the homogenized equation, which is obtained by the unfolding technique.