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Homogenization results for a class of parabolic equations with a non-local interface condition via time-periodic unfolding

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Abstract

We study the thermal properties of a composite material in which a periodic array of finely mixed perfect thermal conductors is inserted. The suitable model describing the behaviour of such physical materials leads to the so-called equivalued surface boundary value problem. To analyze the overall conductivity of the composite medium (when the size of the inclusions tends to zero), we make use of the homogenization theory, employing the unfolding technique. The peculiarity of the problem under investigation asks for a particular care in developing the unfolding procedure, giving rise to a non-standard two-scale problem.

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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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Correspondence to M. Amar.

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Amar, M., Andreucci, D., Gianni, R. et al. Homogenization results for a class of parabolic equations with a non-local interface condition via time-periodic unfolding. Nonlinear Differ. Equ. Appl. 26, 52 (2019). https://doi.org/10.1007/s00030-019-0592-4

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  • DOI: https://doi.org/10.1007/s00030-019-0592-4

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