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.

Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator / Amar, Micol; Andreucci, Daniele; Gianni, Roberto; Timofte, Claudia. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 59:3(2020). [10.1007/s00526-020-01749-x]

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

Micol Amar
;
Daniele Andreucci;
2020

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1251547
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