69 citations · 105 across the 5 of their papers we have counts for
3 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,…
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…