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We study a concentration and homogenization problem modelling electricalconduction in a composite material. The novelty of the problem is due to thespecific scaling of the physical quantities characterizing the dielectriccomponent of the composite. This leads to the appearance of a peculiardisplacement 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.

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