Derivation of a homogenized two-temperature model from the heat equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, p. 1583-1613
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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 : https://doi.org/10.1051/m2an/2014011
Classification:  35K05,  35B27,  76T05,  35Q79,  76M50
Keywords: heat equation, homogenization, infinite diffusion limit, thermal nonequilibrium models
@article{M2AN_2014__48_6_1583_0,
     author = {Desvillettes, Laurent and Golse, Fran\c cois and Ricci, Valeria},
     title = {Derivation of a homogenized two-temperature model from the heat equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {6},
     year = {2014},
     pages = {1583-1613},
     doi = {10.1051/m2an/2014011},
     mrnumber = {3264366},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_6_1583_0}
}
Desvillettes, Laurent; Golse, François; Ricci, Valeria. Derivation of a homogenized two-temperature model from the heat equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, pp. 1583-1613. doi : 10.1051/m2an/2014011. http://www.numdam.org/item/M2AN_2014__48_6_1583_0/

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