Homogenization of a thermal problem with flux jump

Renata  Bunoiu; Claudia  Timofte; Renata  Bunoiu; Claudia  Timofte

doi:10.3934/nhm.2016009

Networks and Heterogeneous Media

2016, Volume 11, Issue 4: 545-562. doi: 10.3934/nhm.2016009

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Homogenization of a thermal problem with flux jump

Renata Bunoiu ^{1
,},
Claudia Timofte ^{2
,}

1.
Institut Élie Cartan de Lorraine, CNRS, UMR 7502, Université de Lorraine, Metz, 57045
2.
University of Bucharest, Faculty of Physics, Bucharest-Magurele, P.O. Box MG-11

Received: 01 December 2015
Primary: 35B27, 80M35; Secondary: 80M40.

The goal of this paper is to analyze, through homogenization techniques, the effective thermal transfer in a periodic composite material formed by two constituents, separated by an imperfect interface where both the temperature and the flux exhibit jumps. Following the hypotheses on the flux jump, two different homogenized problems are obtained. These problems capture in various ways the influence of the jumps: in the homogenized coefficients, in the right-hand side of the homogenized problem, and in the correctors.
- Homogenization,
- imperfect interface,
- the periodic unfolding method
Citation: Renata Bunoiu, Claudia Timofte. Homogenization of a thermal problem with flux jump[J]. Networks and Heterogeneous Media, 2016, 11(4): 545-562. doi: 10.3934/nhm.2016009

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Abstract

The goal of this paper is to analyze, through homogenization techniques, the effective thermal transfer in a periodic composite material formed by two constituents, separated by an imperfect interface where both the temperature and the flux exhibit jumps. Following the hypotheses on the flux jump, two different homogenized problems are obtained. These problems capture in various ways the influence of the jumps: in the homogenized coefficients, in the right-hand side of the homogenized problem, and in the correctors.

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