Speaker
Description
We present a result on local well posedness for a highly nonlocal nonlinear diffusion–adhesion system \cite{RZ}. Macroscopic systems of this type were previously obtained through upscaling \cite{ZR} and can account for the effect of microscopic receptor binding dynamics in cell–cell adhesion. The system couples an integro PDE featuring degenerate diffusion of porous medium type and nonlocal adhesion with a novel nonlinear integral equation. The approach is based on decoupling the system and using Banach’s fixed point theorem to solve each of the two equations individually and subsequently the full coupled system. A key challenge lies in identifying a suitable functional setting. One of the main results is the local well posedness of the integral equation with a Radon measure as parameter. The analysis of this equation employs the Kantorovich–Rubinstein norm, marking what appears to be the first use of this norm in the study of a nonlinear integral equation. For details of a multiscale derivation of models of this kind, we refer to \cite{ZR} and to the talk “A cell–cell adhesion model: a multiscale derivation” in this conference.
Bibliography
@article{RZ,
title = {Local {Well}-{Posedness} for a {Novel} {Nonlocal} {Model} for {Cell}-{Cell} {Adhesion} via {Receptor} {Binding}},
volume = {57},
issn = {0036-1410, 1095-7154},
url = {https://epubs.siam.org/doi/10.1137/24M1667518},
doi = {10.1137/24M1667518},
language = {en},
number = {4},
urldate = {2026-03-22},
journal = {SIAM Journal on Mathematical Analysis},
author = {Rajendran, Mabel Lizzy and Zhigun, Anna},
month = aug,
year = {2025},
pages = {4016--4067},
}
@article{ZR,
title = {Modelling non-local cell-cell adhesion: a multiscale approach},
volume = {88},
issn = {0303-6812, 1432-1416},
shorttitle = {Modelling non-local cell-cell adhesion},
doi = {10.1007/s00285-024-02079-8},
number = {5},
urldate = {2026-03-22},
journal = {Journal of Mathematical Biology},
author = {Zhigun, Anna and Rajendran, Mabel Lizzy},
month = may,
year = {2024},
pages = {55},
}
