Free boundary limits of coupled bulk-surface models for receptor-ligand interactions on evolving domains
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.16522
- arXiv:
- arXiv:2407.16522
- Bibcode:
- 2024arXiv240716522A
- Keywords:
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- Mathematics - Analysis of PDEs