Optimal convergence rate for Mullins-Sekerka evolution in the plane

Wenhui Shi (RWTH Aachen) #

The Mullins–Sekerka evolution is a free boundary problem arising in phase transition and can be viewed as the sharp-interface limit of the Cahn–Hilliard equation. It inherits a natural gradient flow structure, which provides a powerful framework for its analysis.

In this talk, I will revisit the HED method, which is based on the interplay between the distance, the energy, and the energy dissipation, for the Mullins–Sekerka evolution in the plane. I will show how this method can be used to establish the sharp convergence rate of solutions toward a flat limiting interface. This is based on joint work with Maria Westdickenberg and Michael Westdickenberg.