70 citations · 244 across the 29 of their papers we have counts for
6 papers · 1 filter
A Stefan problem on an evolving surface
Amal Alphonse, Charles M. Elliott
We formulate a Stefan problem on an evolving hypersurface and study the well-posedness of weak solutions given data. To do this, we first develop function spaces and results…
On some linear parabolic PDEs on moving hypersurfaces
Amal Alphonse, Charles M. Elliott, Björn Stinner
We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation,…
Optimal control of elliptic PDEs on surfaces of codimension 1
C. Brett, A. S. Dedner, C. M. Elliott
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, w…
A computational approach to an optimal partition problem on surfaces
Charles M. Elliott, Thomas Ranner
We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplace--Beltrami operator eigenvalues…
Time-periodic solutions of advection-diffusion equations on moving hypersurfaces
Charles M. Elliott, Hans Fritz
In this paper we study time-periodic solutions to advection-diffusion equations of a scalar quantity on a periodically moving -dimensional hypersurface $Γ(t) \subset \mathbb…
An abstract framework for parabolic PDEs on evolving spaces
Amal Alphonse, Charles M. Elliott, Björn Stinner
We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces. This theory…