Geometric Flows and Phase Transitions in Heterogeneous Media
Speaker: Prof. Dr. Irene Fonseca
Affiliation: Carnegie Mellon University, USA
Abstract: We present the first unconditional convergence results for an Allen-Cahn type bi-stable reaction diffusion equation in a periodic medium.
Our limiting dynamics are given by an analog for anisotropic mean curvature flow of the formulation due to Ken Brakke.
As an essential ingredient in the analysis, we obtain an explicit expression for the effective surface tension, which dictates the limiting anisotropic mean curvature.
This allows us to demonstrate the regularity of the limiting surface tension. This is joint work with Rustum Choksi (McGill), Jessica Lin (McGill), and Raghavendra Venkatraman (CMU).