Effective behavior of a time-oscillating parabolic system with non-local and equi-valued interface conditions

In this paper, we study the homogenization of a heat diffusion problem in a two-phase composite material with imperfect contact conditions on the interface separating its constituents. More precisely, we consider an equi-valued interface condition and a non-local condition, which involves a time-oscillating amplitude factor. We perform a homogenization process, leading to three different macroscopic models, depending on the value of a scaling parameter appearing in the amplitude factor.