On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility
Analysis of PDEs
2023-10-09 v1
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.
Cite
@article{arxiv.2010.04659,
title = {On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility},
author = {Shibin Dai and Qiang Liu and Toai Luong and Keith Promislow},
journal= {arXiv preprint arXiv:2010.04659},
year = {2023}
}