Homogenization of a non-linear 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 comparable heat capacities and conductivities, separated by a third material with thickness of the same order, as the basic periodicity cell but having a much lower conductivity such that the resulting interstitial heat flow is scaled by a factor tending to zero with a rate lambda = lambda(epsilon). The heat flux vectors a(j), j = 1, 2, 3 are non-linear, monotone functions of the temperature gradient. The heat capacities c(j)(x) are positive, but may vanish at some subsets such that the problem can be degenerate (parabolic-elliptic). We show that the critical value of the problem is delta = lim(epsilon -> 0) epsilon(p)/lambda and identify the homogenized problem depending on whether delta is zero, strictly positive finite or infinite. Copyright (c) 2005 John Wiley & Sons, Ltd.