EVENT DETAILS AND ABSTRACT

Title: Slow Motion of Gradient Flows
Speaker: Professor Maria G. Reznikof
Speaker Info: Princeton University
Brief Description:
Special Note:
Abstract:

Sometimes physical systems exhibit ``metastability,'' in the sense that states get drawn toward so--called metastable states and are trapped near them for a very long time. A familiar example is the one--dimensional Allen Cahn equation: initial data is drawn quickly to a ``multi--kink'' state and the subsequent evolution is exponentially slow. The slow coarsening has been analyzed by Carr-Pego, Fusco-Hale, and Bronsard-Kohn.

In general, what causes metastability? Our main idea is to convert information about the energy landscape (statics) into information about the coarsening rate (dynamics). We give sufficient conditions for a gradient flow system to exhibit metastability. We then apply this abstract framework to give a new analysis of the 1--d Allen Cahn equation. The central ingredient is to establish a certain nonlinear energy--energy--dissipation relationship. One benefit of the method is that it shows that exponential closeness to the multi--kink state is not only propagated, but also generated.

This work is joint with Felix Otto, University of Bonn.