no. 6
Derivation of a homogenized two-temperature model from the heat equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1583-1613.

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat, Collège de France Seminar, vol. II. Paris 1979-1980; vol. 60 of Res. Notes Math. Pitman, Boston, London (1982) 98-138].

DOI : 10.1051/m2an/2014011
Classification : 35K05, 35B27, 76T05, 35Q79, 76M50
Mots clés : heat equation, homogenization, infinite diffusion limit, thermal nonequilibrium models 
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Desvillettes, Laurent; Golse, François; Ricci, Valeria. Derivation of a homogenized two-temperature model from the heat equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1583-1613. doi : 10.1051/m2an/2014011. http://www.numdam.org/articles/10.1051/m2an/2014011/

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