# Past OxPDE Lunchtime Seminar

We study the mean-field models describing the evolution of distributions
of particle radii obtained by taking the small volume fraction limit of
the free boundary problem describing the micro phase separation of
diblock copolymer melts, where micro phase separation consists of an
ensemble of small balls of one component. In the dilute case, we
identify all the steady states and show the convergence of solutions.

Next we study the dynamics for a free boundary problem in two dimension,
obtained as a gradient flow of Ohta- Kawasaki free energy, in the case
that one component is a distorted disk with a small volume fraction. We
show the existence of solutions that a small, almost circular interface
moves along a curve determined via a Green’s function of the domain.
This talk is partly based on a joint work with Xiaofeng Ren.