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math.AP2016★ 1 cited
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes
Charles M. Elliott, Hans Fritz, Graham Hobbs
In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is sui…
math.AP2014
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…
math.AP2014★ 69 cited
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…