Volume 4, Issue 3
Homogenization of an Elliptic System Involving Non-Local and Equi-Valued Interface Conditions

Micol Amar, Daniele Andreucci & Claudia Timofte

Commun. Math. Anal. Appl., 4 (2025), pp. 347-367.

Published online: 2025-09

Export citation
  • Abstract

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 $α > −1,$ 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.

  • AMS Subject Headings

35B27, 35J25, 35Q79

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMAA-4-347, author = {Amar , MicolAndreucci , Daniele and Timofte , Claudia}, title = {Homogenization of an Elliptic System Involving Non-Local and Equi-Valued Interface Conditions}, journal = {Communications in Mathematical Analysis and Applications}, year = {2025}, volume = {4}, number = {3}, pages = {347--367}, abstract = {

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 $α > −1,$ 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.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2025-0009}, url = {http://global-sci.org/intro/article_detail/cmaa/24333.html} }
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 -

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 $α > −1,$ 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.

Amar , MicolAndreucci , Daniele and Timofte , Claudia. (2025). Homogenization of an Elliptic System Involving Non-Local and Equi-Valued Interface Conditions. Communications in Mathematical Analysis and Applications. 4 (3). 347-367. doi:10.4208/cmaa.2025-0009
Copy to clipboard
The citation has been copied to your clipboard