Analysis and PDE Seminar: Convergence of phase-field models and thresholding schemes for multi-phase mean curvature flow

Seminar | October 2 | 4:10-5 p.m. | 740 Evans Hall

 Tim Laux, UC Berkeley

 Department of Mathematics

The thresholding scheme is a time discretization for mean curvature flow. Recently, Esedoglu and Otto showed that thresholding can be interpreted as minimizing movements for an energy that Gamma-converges to the total interfacial area. In this talk I'll present new convergence results, 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. Furthermore, I will present a similar result for the vector-valued Allen-Cahn equation.

This talk encompasses joint works with Felix Otto, Thilo Simon, and Drew Swartz.