70 citations · 244 across the 29 of their papers we have counts for
4 papers · 1 filter
Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
Charles M. Elliott, Thomas Ranner, Chandrasekhar Venkataraman
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a ma…
A Variational Approach to Particles in Lipid Membranes
Charles M. Elliott, Carsten Gräser, Graham Hobbs +2
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspecti…
Well-posedness of a fractional porous medium equation on an evolving surface
Amal Alphonse, Charles M. Elliott
We investigate the existence, uniqueness, and -contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the…
Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient
Klaus Deckelnick, Charles M. Elliott, Vanessa Styles
We propose a double obstacle phase field approach to the recovery of piece-wise constant diffusion coefficients for elliptic partial differential equations. The approach to this in…