TY - JOUR
T1 - Homogenization of an Elliptic System Involving Non-Local and Equi-Valued Interface Conditions
AU - Amar , Micol
AU - Andreucci , Daniele
AU - Timofte , Claudia
JO - Communications in Mathematical Analysis and Applications
VL - 3
SP - 347
EP - 367
PY - 2025
DA - 2025/09
SN - 4
DO - http://doi.org/10.4208/cmaa.2025-0009
UR - https://global-sci.org/intro/article_detail/cmaa/24333.html
KW - Periodic homogenization, non-local transmission conditions, equi-valued interface conditions, elliptic systems.
AB - <p style="text-align: justify;">In this paper, we analyze the effective behaviour of the solution of
an elliptic problem in a two-phase composite material with non-standard imperfect contact conditions between its constituents. More specifically, we consider on the interface an equi-valued surface condition and a non-local flux
condition involving a scaling parameter $α.$ We perform a homogenization procedure by using the periodic unfolding technique. As a result, we obtain two
different effective models, depending on the scaling parameter $α.$ More precisely, in the case $α &gt; −1,$ we are led to a standard Dirichlet problem for an
elliptic equation, while in the case $α = −1,$ we get a bidomain system, consisting in the coupling of an elliptic equation with an algebraic one.</p>