Homogenization of a degenerate parabolic problem in a highly heterogeneous periodic medium

We consider the homogenization of a time-dependent heat transfer problem in a highly heterogeneous periodic medium made of two connected components having heat capacities c(alpha)(x) and heat conductivities alpha(alpha) (x), alpha = 1, 2 of order one, separated by a third material with thickness of the same order epsilon than the basic periodicity cell having heat capacity c(3)(x) and conductivity lambdaa(3)(x) where a(3) is of order one and lambda tends to zero with the size E of the elementary cell. We assume only that c(i)(x) greater than or equal to 0, i = 1, 2, 3 almost everywhere, such that the problem can be degenerate (parabolic-elliptic). We show that the critical value of the problem is delta = limepsilon-->epsilon(2)/lambda and identify the homogenized problem depending on delta is zero, strictly positive finite or infinite. (C) 2004 Elsevier Ltd. All rights reserved.