The Mathematics of Coarsening
by
Robert V. Kohn
Courant Institute

I will discuss surface-energy-driven coarsening of two-phase microstructures. Such coarsening is observed in many physical systems. Experiments and simulations suggest that solutions are in some sense statistically self-similar. There is, however, virtually nothing known with mathematical rigor. I will introduce this topic, then present recent joint work with Felix Otto (Comm. Math. Phys. 2002).

Our main accomplishment is an upper bound on the coarsening rate, consistent with the conjectured self-similar behavior. Our work is also interesting for its viewpoint, which is new and potentially applicable to many other problems. I will close with one such application, to epitaxial growth -- joint work with Xiaodong Yan (Comm. Pure Appl. Math. 2003).

Date received: October 28, 2003