Weak Solutions For The Functionalized Cahn-Hilliard Equation With Degenerate Mobility

The functionalized Cahn-Hilliard free energy describes phase separation in mixtures of amphiphilic molecules in solvent. Applications to highly amphiphilic molecules such as lipids requires degenerate diffusion that eliminates bulk diffusion, resulting in surface driven diffusion. We study the existence of weak solutions of a gradient flow of the functionalized Cahn-Hilliard equation that incorporates degenerate mobility, capturing solutions as limits of the weak solution for equations with non-degenerate mobilities.