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arXiv · 2001.07780

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

Micol Amar·Daniele Andreucci·Roberto Gianni·Claudia Timofte
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Abstract

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.

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Micol Amar, Daniele Andreucci, Roberto Gianni, Claudia Timofte. 2020-01-21. Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator. https://arxiv.org/abs/2001.07780

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