Faculty of Transport and Traffic Sciences
University of Zagreb, Croatia
email: tfratrovic@fpz.unizg.hr
Department of Mathematics
Faculty of Science
University of Zagreb, Croatia
email: emarusic@math.hr
Tomislav Fratrovic, Eduard Marusic-Paloka
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.
Submitted July 15, 2026. Published August 17, 2026.
Math Subject Classifications: 35B27, 35J05, 74Q05, 80M40.
Key Words: Homogenization; asymptotic expansion; boundary layers; macroscopic model;
effective interface condition.
DOI: 10.58997/ejde.2026.61
Show me the PDF file (366 KB), TEX file for this article.
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Tomislav Fratrovic Faculty of Transport and Traffic Sciences University of Zagreb, Croatia email: tfratrovic@fpz.unizg.hr |
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Eduard Marusic-Paloka Department of Mathematics Faculty of Science University of Zagreb, Croatia email: emarusic@math.hr |
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