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.
Accepted:
Published online:
Mots-clés : Transferts thermiques, Milieu pédiodique fortement hétérogène
Mongi Mabrouk 1; Ahmed Boughammoura 2
@article{CRMECA_2003__331_6_415_0, author = {Mongi Mabrouk and Ahmed Boughammoura}, title = {Homogenization of a degenerate parabolic problem in a highly heteregeneous medium}, journal = {Comptes Rendus. M\'ecanique}, pages = {415--421}, publisher = {Elsevier}, volume = {331}, number = {6}, year = {2003}, doi = {10.1016/S1631-0721(03)00088-3}, language = {en}, }
TY - JOUR AU - Mongi Mabrouk AU - Ahmed Boughammoura TI - Homogenization of a degenerate parabolic problem in a highly heteregeneous medium JO - Comptes Rendus. Mécanique PY - 2003 SP - 415 EP - 421 VL - 331 IS - 6 PB - Elsevier DO - 10.1016/S1631-0721(03)00088-3 LA - en ID - CRMECA_2003__331_6_415_0 ER -
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/
[1] Homogenization of a heat transfer problem in a highly heteregeneous periodic medium, Int. J. Engrg. Sci., Volume 40 (2002), pp. 1233-1250
[2] Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Math. Surveys Monographs, 49, American Mathematical Society, Providence, RI, 1997
[3] On the problem of the process of propagation of heat in heteregeneous media, Izv. Akad. Nauk SSSR Ser. Geogr., Volume 1 (1948)
[4] Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks strata, J. Appl. Math. Mech., Volume 24 (1960), pp. 852-864
Cited by Sources:
Comments - Policy