70 citations · 244 across the 29 of their papers we have counts for
39 papers
Bulk-surface systems on evolving domains
Diogo Caetano, Charles M. Elliott, Bao Quoc Tang
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the globa…
Regularisation and separation for evolving surface Cahn-Hilliard equations
Diogo Caetano, Charles M. Elliott, Maurizio Grasselli +1
We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in , as well as a related…
Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces
Charles M. Elliott, Harald Garcke, Balázs Kovács
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvatur…
Models for information propagation on graphs
Oliver R. A. Dunbar, Charles M. Elliott, Lisa Maria Kreusser
We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of \emph{kno…
Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs
Amal Alphonse, Diogo Caetano, Ana Djurdjevac +1
We develop a functional framework suitable for the treatment of partial differential equations and variational problems on evolving families of Banach spaces. We propose a definiti…
Cahn-Hilliard equations on an evolving surface
Diogo Caetano, Charles M. Elliott
We describe a functional framework suitable to the analysis of the Cahn-Hilliard equation on an evolving surface whose evolution is assumed to be given \textit{a priori}. The model…