Free boundary limits of coupled bulk-surface models for receptor-ligand interactions on evolving domains

TL;DR

This paper derives new free boundary problems from coupled bulk-surface reaction-diffusion models for ligand-receptor interactions on evolving domains, with implications for cell biology and numerical simulations.

Contribution

It introduces novel free boundary limits as Stefan-type problems on evolving hypersurfaces, extending previous models to include domain evolution and providing analytical and numerical insights.

Findings

New free boundary problems derived as limits of reaction-diffusion systems

Application of $L^ Infty$-estimates and De Giorgi iterations in evolving domains

Numerical simulations supporting theoretical results

Abstract

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type problems on an evolving hypersurface. Our results are new even in the setting where there is no domain evolution. The models are of particular relevance to a number of applications in cell biology. The analysis utilises $L^\infty$-estimates in the manner of De Giorgi iterations and other technical tools, all in an evolving setting. We also report on numerical simulations.