Communications in Mathematical Sciences

Volume 15 (2017)

Number 3

On the homogenization of a two-conductivity problem with flux jump

Pages: 745 – 763

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n3.a8

Authors

Renata Bunoiu (Institut Elie Cartan de Lorraine and CNRS, Université de Lorraine, Metz, France)

Claudia Timofte (Faculty of Physics, University of Bucharest, Bucharest-Magurele, Romania)

Abstract

In this paper, we study the homogenization of a thermal diffusion problem in a highly heterogeneous medium formed by two constituents. The main characteristics of the medium are the discontinuity of the thermal conductivity over the domain as we go from one constituent to another and the presence of an imperfect interface between the two constituents, where both the temperature and the flux exhibit jumps. The limit problem, obtained via the periodic unfolding method, captures the influence of the jumps in the limit temperature field, in an additional source term, and in the correctors, as well.

Keywords

homogenization, imperfect interface, the periodic unfolding method

2010 Mathematics Subject Classification

35B27, 80M35, 80M40

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