Title :

Effective interface conditions for a porous medium type problem

Author(s) :

Ciavolella, Giorgia [Auteur]
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
David, Noemi [Auteur]
Université de Lyon
Institut Camille Jordan [ICJ]
Modélisation mathématique, calcul scientifique [MMCS]
Poulain, Alexandre [Auteur correspondant]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sorbonne Université [SU]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Modelling and Analysis for Medical and Biological Applications [MAMBA]

Journal title :

Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications

Publisher :

European Mathematical Society

Publication date :

2024-02-06

ISSN :

1463-9963

English keyword(s) :

Membrane boundary conditions
Effective interface
Porous medium equation
Nonlinear reaction-diffusion equations
Tumour growth models

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

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 ...
Show more >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 to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero.Show less >

Language :

Anglais

Popular science :

Non

European Project :

Asymptotic approach to spatial and dynamical organizations
International Doctoral Training in Mathematical Sciences in Paris

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL