WIAS Preprint No. 3122, (2024)

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



Authors

  • Alphonse, Amal
    ORCID: 0000-0001-7616-3293
  • Caetano, Diego
  • Elliott, Charles M.
  • Venkataraman, Chandrasekhar

2020 Mathematics Subject Classification

  • 35K57 35R35 35R37 92C37 58J35

Keywords

  • Free boundary problem, parabolic PDE, evolving domain, Stefan problem, reaction-diffusion system, ligand-receptor modelling

DOI

10.20347/WIAS.PREPRINT.3122

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-estimates in the manner of De Giorgi iterations and other technical tools, all in an evolving setting. We also report on numerical simulations.

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