Speaker
Description
In the first part of the talk, we consider coupled bulk-surface reaction-diffusion systems modelling receptor-ligand dynamics on an evolving domain. In biologically relevant regimes, we derive various novel free-boundary problems as limits of the model. 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 relevance to applications in cell biology. Numerical simulations illustrating the convergence towards free-boundary problems will be presented. This part of the talk is based on joint work with Amal Alphonse (WIAS), Diogo Caetano, and Charlie Elliott (both Warwick)
In the second part of the talk, we discuss an evolving surface finite element method (ESFEM) for solving the two-phase Stefan problem on an evolving surface. In particular, we discuss the error analysis for an ESFEM discretisation of the enthalpy formulation of the two-phase Stefan problem. We will also discuss some qualitative properties of solutions to the enthalpy formulation on an evolving surface. This part is joint work with Philip Herbert (Sussex) and Tom Sales (UCL).