Communications in Mathematical Sciences
Volume 12 (2014)
Colliding interfaces in old and new diffuse-interface approximations of Willmore-flow
Pages: 125 – 147
This paper is concerned with difuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards interfaces with corners can occur that do not necessarily describe the adequate sharp-interface dynamics. We therefore propose and investigate alternative diffuse-interface approximations that lead to a different and more regular behavior if interfaces collide. These dynamics are derived from approximate energies that converge to the $L_1$-lower-semicontinuous envelope of the Willmore energy, which is in general not true for the more standard Willmore approximation.
diffuse-interface, Willmore flow, elastica energy, topological change
2010 Mathematics Subject Classification
49J45, 53C44, 74S05