The periodic unfolding method for a class of parabolic problems with imperfect interfaces

Abstract

In this paper, we use the adapted periodic unfolding method to study the homogeniza- tion and corrector problems for the parabolic problem in a two-component composite with e-periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is propor- tional to the conormal derivative via a function of order e γ with γ ≤− 1. We give the homogenization results which include those obtained by Jose in (Rev. Roum. Math. Pures Appl. 54 (2009) 189-222). We also get the corrector results.