On the Sharp Interface Limit of a Model for Phase Separation on Biological Membranes
Analysis of PDEs
2019-02-05 v2
Abstract
We rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed by Garcke et al. to weak (varifold) solutions of the corresponding sharp-interface problem for a suitable subsequence. In the system a Cahn-Hilliard type equation on the boundary of a domain is coupled to a diffusion equation inside the domain. The proof builds on techniques developed by X. Chen for the corresponding result for the Cahn-Hilliard equation.
Keywords
Cite
@article{arxiv.1811.12489,
title = {On the Sharp Interface Limit of a Model for Phase Separation on Biological Membranes},
author = {Helmut Abels and Johannes Kampmann},
journal= {arXiv preprint arXiv:1811.12489},
year = {2019}
}
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31 pages