Analysis Seminar

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Convergence of Phase-Field Models and Thresholding Schemes to Multi-Phase Mean-Curvature Flow

Speaker: Tim Laux, Max Planck Institute, Leipzig

Location: Warren Weaver Hall 1314

Date: Monday, November 21, 2016, 11 a.m.

Synopsis:

The thresholding scheme -- a time discretization for mean curvature flow -- was introduced by Merriman, Bence and Osher. In this talk I'll present new convergence results for modern variants of the scheme, in particular in the multi-phase case with arbitrary surface tensions. The main result establishes convergence to a weak formulation of (multi-phase) mean curvature flow in the BV-framework of sets of finite perimeter. The methods are then extended to incorporate external forces and a volume constraint. Furthermore, I will present a similar result for the vector-valued Allen-Cahn Equation. This talk encompasses joint work with Felix Otto, Thilo Simon, and Drew Swartz (Booz Allen Hamilton).