A Cahn-Hilliard equation with singular diffusion
Analysis of PDEs
2012-06-26 v1
Abstract
In the present work, we address a class of Cahn-Hilliard equations characterized by a singular diffusion term. The problem is a simplified version with constant mobility of the Cahn-Hilliard-de Gennes model of phase separation in binary, incompressible, isothermal mixtures of polymer molecules. It is proved that, for any final time T, the problem admits a unique energy type weak solution, defined over (0,T). For any s > 0 such solution is classical in the sense of belonging to a suitable Hoelder class over (s,T), and enjoys the property of being separated from the singular values corresponding to pure phases.
Cite
@article{arxiv.1206.5604,
title = {A Cahn-Hilliard equation with singular diffusion},
author = {Giulio Schimperna and Irena Pawlow},
journal= {arXiv preprint arXiv:1206.5604},
year = {2012}
}