Robert Kohn, Courant Institute, NYU
"Upper Bounds on Coarsening Rates"
This talk addresses energy-driven coarsening, in the context of (a) phase separation (joint work with Felix Otto), and (b) epitaxial growth (joint work with Xiaodong Yan). Numerical and physical experiments suggest statistically self-similar behavior, however virtually nothing is known with mathematical rigor. I will discuss a new scheme for proving upper bounds on the coarsening rate, consistent with the conjectured self-similar behavior. The method combines (i) suitable energy estimates, (ii) a sort of isoperimetric inequality, and (iii) an ODE lemma.
THURSDAY, October 24, 2002