Homogenization of a degenerate parabolic problem in a highly heteregeneous medium
Mongi Mabrouk, Ahmed Boughammoura · Comptes Rendus Mécanique · 2003
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 .