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

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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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Acknowledgements

The first author is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The second author is member of the Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM). The last author wishes to thank Dipartimento di Scienze di Base e Applicate per l’Ingegneria for the warm hospitality and Università “La Sapienza” of Rome for the financial support.

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Authors and Affiliations

  1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza - Università di Roma, Via A. Scarpa 16, 00161, Rome, Italy

    M. Amar & D. Andreucci

  2. Dipartimento di Matematica ed Informatica, Università di Firenze, Via Santa Marta 3, 50139, Florence, Italy

    R. Gianni

  3. Faculty of Physics, University of Bucharest, P.O. Box MG-11, Bucharest, Romania

    C. Timofte

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  1. M. Amar
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  2. D. Andreucci
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  3. R. Gianni
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  4. C. Timofte
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Corresponding author

Correspondence to M. Amar.

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Communicated by L. Ambrosio.

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Amar, M., Andreucci, D., Gianni, R. et al. Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace–Beltrami operator. Calc. Var. 59, 99 (2020). https://doi.org/10.1007/s00526-020-01749-x

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