Homogenization of composite media with non-standard transmission conditions

In this paper we study the homogenization limits for the steady state of a diffusion problem in a composite medium made up by two different materials: a host material and the inclusion material which is disposed in a periodic array and has a typical length scale <euro>. On the interface separating the two phases two different sets of non-standard transmission conditions are assigned (thus originating two different systems of partial differential equations). As <euro> tends to zero a hierarchy of homogenization problem related to such interface conditions is studied and the physical properties of the various limits are discussed. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org /licenses /by-nc-nd /4 .0/).