69 citations · 105 across the 5 of their papers we have counts for
8 papers
Transmission problems and domain decompositions for non-autonomous parabolic equations on evolving domains
Amal Alphonse, Ana Djurdjevac, Emil Engström +1
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numeric…
Free boundary limits of coupled bulk-surface models for receptor-ligand interactions on evolving domains
Amal Alphonse, Diogo Caetano, Charles M. Elliott +1
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting…
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…
A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity and convergence to equilibrium
Amal Alphonse, Charles M. Elliott, Joana Terra
We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The…
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…
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…