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

摘要

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_α(x) and heat conductivities a_α(x), α = 1,2 of order one, separated by a third material with thickness of the same order ε than the basic periodicity cell having heat capacity c_3(x) and conductivity λa_3(x) where a_3 is of order one and λ tends to zero with the size ε of the elementary cell. We assume only that c_i(x) ≥ 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 δ = lim_(ε→0) ε~2/λ identify the homogenized problem depending on δ is zero, strictly positive finite or infinite.