1Sorbonne Université, Inria, Université de Paris, France; Università di Roma “Tor Vergata”, Italy; Université de Bordeaux, Inria, Talence, France 2Sorbonne Université, Inria, Université de Paris, France; Universitá di Bologna, Italy; Université de Lyon 1, Villeurbanne, France 3Sorbonne Université, Inria, Université de Paris, France; Université de Lille, France
Interfaces and free boundaries, Tome 26 (2024) no. 2, pp. 161-188
Motivated by biological applications on tumour invasion through thin membranes, we study a porous medium type equation where the density of the cell population evolves under Darcy’s law, assuming continuity of both the density and flux velocity on the thin membrane which separates two domains. The drastically different scales and mobility rates between the membrane and the adjacent tissues lead to consider the limit as the thickness of the membrane approaches zero. We are interested in recovering the effective interface problem and the transmission conditions on the limiting zero-thickness surface, formally derived by Chaplain et al. (2019), which are compatible with nonlinear generalized Kedem–Katchalsky ones. Our analysis relies on a priori estimates and compactness arguments as well as on the construction of a suitable extension operator, which allows us to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero.
1
Sorbonne Université, Inria, Université de Paris, France; Università di Roma “Tor Vergata”, Italy; Université de Bordeaux, Inria, Talence, France
2
Sorbonne Université, Inria, Université de Paris, France; Universitá di Bologna, Italy; Université de Lyon 1, Villeurbanne, France
3
Sorbonne Université, Inria, Université de Paris, France; Université de Lille, France
Giorgia Ciavolella; Noemi David; Alexandre Poulain. Effective interface conditions for a porous medium type problem. Interfaces and free boundaries, Tome 26 (2024) no. 2, pp. 161-188. doi: 10.4171/ifb/505
@article{10_4171_ifb_505,
author = {Giorgia Ciavolella and Noemi David and Alexandre Poulain},
title = {Effective interface conditions for a porous medium type problem},
journal = {Interfaces and free boundaries},
pages = {161--188},
year = {2024},
volume = {26},
number = {2},
doi = {10.4171/ifb/505},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/505/}
}
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AU - Noemi David
AU - Alexandre Poulain
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