Title: Convergence and metastability of (mildly) nonconvex gradient flows
Abstract: Together with Felix Otto (MPI MIS), Richard Schubert (University of Bonn), and other collaborators, we have developed different energy-based methods to capture convergence and metastability of gradient flows. Among other things, we have used these methods to better understand dynamic metastability in the 1-d Allen Cahn (second order) and Cahn Hilliard (fourth order) equations. In this talk we will give an overview of the methods, recalling the properties and challenges of the fourth order equation and highlighting the features associated to different choices of distance.