The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by a variational minimization principle.
Cite this article
Pierluigi Colli, Philippe Laurençot, A phase-field approximation of the Willmore flow with volume constraint. Interfaces Free Bound. 13 (2011), no. 3, pp. 341–351