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Peer-reviewedCC BYElectronic Journal of Differential Equations

Interface condition for the Poisson equation in a partially porous medium

  • Tomislav Fratrovic1
  • Eduard Marusic-Paloka1
  1. 1Univ. of Zagreb, Croatia
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Abstract

In this article, we derive a new effective interface condition between two parts of a partially porous medium. We study the steady-state Poisson equation in a two-dimensional domain that combines an upper porous part with a periodic microstructure and a lower free region. Using the homogenization approach and a formal asymptotic expansion, we establish a second-order correction to the classical interface condition that accounts for microscale effects, including those arising from both the local flux and the source term redistribution across the interface. This refinement is essential for high-precision applications in which the pore size is small but not negligible compared to the system scale.

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Cite

BibTeXRIS
BibTeX
@article{fratrovic2026interface,
  title = {{Interface condition for the Poisson equation in a partially porous medium}},
  author = {Tomislav Fratrovic and Eduard Marusic-Paloka},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = aug,
  url = {http://ejde.math.txstate.edu/Volumes/2026/61/abstr.html},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Interface condition for the Poisson equation in a partially porous medium
AU  - Tomislav Fratrovic
AU  - Eduard Marusic-Paloka
PY  - 2026
DA  - 2026/08/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/61/abstr.html
AB  - In this article, we derive a new effective interface condition between two parts of a partially porous medium. We study the steady-state Poisson equation in a two-dimensional domain that combines an upper porous part with a periodic microstructure and a lower free region. Using the homogenization approach and a formal asymptotic expansion, we establish a second-order correction to the classical interface condition that accounts for microscale effects, including those arising from both the local flux and the source term redistribution across the interface. This refinement is essential for high-precision applications in which the pore size is small but not negligible compared to the system scale.
SN  - 1072-6691
ER  -