Degenerate Cahn-Hilliard equation: From nonlocal to local
Analysis of PDEs
2022-12-19 v3
Abstract
There has been recently an important interest in deriving rigorously the Cahn-Hilliard equation from the nonlocal equation, also called aggregation equation. So far, only non-degenerate mobilities were treated. Since we are motivated by models for the biomechanics of living tissues, it is useful to include degenerate motilities. In this framework, we present a new method to show the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation. The method includes the use of nonlocal Poincar\'e and compactness inequalities.
Keywords
Cite
@article{arxiv.2208.08955,
title = {Degenerate Cahn-Hilliard equation: From nonlocal to local},
author = {Charles Elbar and Jakub Skrzeczkowski},
journal= {arXiv preprint arXiv:2208.08955},
year = {2022}
}