Degenerate Diffusion in Phase Separations
The Cahn-Hilliard equation is a widely used phenomenological diffuse-interface model for the simulations of phase separation and microstructure evolution in binary systems. We consider a popular form of the equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes both theoretical analysis and accurate numerical simulations challenging. In this talk, we discuss three aspects of the equation: 1. theoretical predictions on the coarsening dynamics based on asymptotic analysis; 2. numerical simulations that confirm the theoretical predictions; 3. the existence of weak solutions that potentially accommodate the features predicted by asymptotic analysis and exhibited in numerical simulations.