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Homogenization of a degenerate parabolic problem in a highly heteregeneous medium

โœ Scribed by Mongi Mabrouk; Ahmed Boughammoura

Publisher
Elsevier Science
Year
2003
Tongue
French
Weight
125 KB
Volume
331
Category
Article
ISSN
1631-0721

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โœฆ Synopsis

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 c ฮฑ (x) and heat conductivities a ฮฑ (x), ฮฑ = 1, 2, of order one, separated by a third material with thickness of order ฮต the size of the basic periodicity cell, but with conductivity ฮปa 3 (x) where a 3 = O(1) and ฮป tends to zero with ฮต. Assuming only that c i (x) 0 a.e., such that the problem can degenerate (parabolicelliptic), we identify the homogenized problem following the values of ฮด = lim ฮตโ†’0 ฮต 2 /ฮป.

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