Asymptotic analysis for non-local problems in composites with different imperfect contact conditions

We consider a composite material made up of hosting medium containing an ε-periodic array perfect thermal conductors. Comparing with the previous contributions in literature, present paper, inclusions are completely disconnected and form two families dissimilar physical behaviour. More specifically, imperfect contact between obeys different laws, according to types inclusions. The conditions involve small parameter ε positive constants D1,D2. investigate homogenization limit ϵ→0 limits for D1,D2 going 0 or +∞, taken any order, aim find out cases which commute.