Title: Degenerate Diffusion in Phase Separations

Abstract: Phase separations are widely observed phenomena in materials science. One model of phase separation is the Cahn-Hilliard equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes the analysis and accurate numerical simulations challenging. In this talk I will discuss three aspects of the degenerate Cahn-Hilliard equations:
1. the sharp-interface limit via asymptotic analysis, and the dynamics in different time scales;
2. the accurate numerical simulation results that confirm the behavior predicted by asymptotic analysis;
3. the existence of weak solutions for the degenerate Cahn-Hilliard equation.
I will also briefly discuss several directions for further exploration.