Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
Analysis of PDEs
2015-12-01 v1
Abstract
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all of these problems can be obtained as limits of the Cahn-Hilliard related problems. Convergence results and error estimates are proved.
Cite
@article{arxiv.1511.08853,
title = {Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems},
author = {Pierluigi Colli and Takeshi Fukao},
journal= {arXiv preprint arXiv:1511.08853},
year = {2015}
}