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math.AP2014
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,…
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…