Comptes Rendus
Homogenization of a degenerate parabolic problem in a highly heteregeneous medium
Comptes Rendus. Mécanique, Volume 331 (2003) no. 6, pp. 415-421.

We consider the homogenization of a time-dependent heat transfer problem in a highly heteregeneous periodic medium made of two connected components having finite heat capacities cα(x) and heat conductivities aα(x), α=1,2, of order one, separated by a third material with thickness of order ε the size of the basic periodicity cell, but with conductivity λa3(x) where a3=O(1) and λ tends to zero with ε. Assuming only that ci(x)⩾0 a.e., such that the problem can degenerate (parabolic-elliptic), we identify the homogenized problem following the values of δ=limε→0ε2/λ.

Nous considérons un problème de propagation de chaleur dans un milieu périodique fortement hétérogène constitué de deux composantes connexes ayant des capacités calorifiques cα et des conductivités aα comparables, séparés par une couche d'épaisseur d'ordre ε, taille de la cellule de reférence, mais de conductivité λa3, a3 d'ordre un et λ tendant vers zéro avec ε. Sous l'hypothèse ci(y)⩾0 sur les capacités, autorisant une dégénérescence parabolique-elliptique, nous identifions les problèmes homogénéisés suivant les valeurs de δ=limεε2/λ.

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Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00088-3
Keywords: Heat transfer, Heteregeneous periodic medium
Mot clés : Transferts thermiques, Milieu pédiodique fortement hétérogène

Mongi Mabrouk 1; Ahmed Boughammoura 2

1 LMARC UMR 6608, 24, rue de l'épitaphe, 25000 Besançon, France
2 I.P.E.I. Monastir, rue Ebn Eljazzar, 5019 Monastir, Tunisia
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     title = {Homogenization of a degenerate parabolic problem in a highly heteregeneous medium},
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Mongi Mabrouk; Ahmed Boughammoura. Homogenization of a degenerate parabolic problem in a highly heteregeneous medium. Comptes Rendus. Mécanique, Volume 331 (2003) no. 6, pp. 415-421. doi : 10.1016/S1631-0721(03)00088-3. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00088-3/

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[2] R.E. Schowalter Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Math. Surveys Monographs, 49, American Mathematical Society, Providence, RI, 1997

[3] L.I. Rubinstein On the problem of the process of propagation of heat in heteregeneous media, Izv. Akad. Nauk SSSR Ser. Geogr., Volume 1 (1948)

[4] G.I. Barenblatt; I.P. Zheltov; I.N. Kochina Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks strata, J. Appl. Math. Mech., Volume 24 (1960), pp. 852-864

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