On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility
arXiv:2010.04659 · doi:10.1016/j.rinam.2021.100195
Abstract
The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a nonnegative weak solutions of a gradient flow of the Functionalized Cahn-Hilliard equation subject to a degenerate mobility M(u) that is zero for u<=0. Assuming the initial data u0(x) is positive, we construct a weak solution as the limit of solutions corresponding to nondegenerate mobilities and verify that it satisfies an energy dissipation inequality.