Homogenization of a degenerate parabolic problem in a highly heteregeneous medium

Abstract

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 α ( x) and heat conductivities a α ( 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 λa 3( x) where a 3=O(1) and λ tends to zero with ε. Assuming only that c i ( x)⩾0 a.e., such that the problem can degenerate (parabolic-elliptic), we identify the homogenized problem following the values of δ=lim ε→0 ε 2/ λ. To cite this article: M. Mabrouk, A. Boughammoura, C. R. Mecanique 331 (2003).