On the sharp interface limit of a model for phase separation on biological membranes-Reference-Cited by-同舟云学术

On the sharp interface limit of a model for phase separation on biological membranes

Published:2020-11-11 Issue:1 Volume:41 Page:37-60
ISSN:2196-6753
Container-title:Analysis
language:en
Short-container-title:

Author:

Abels Helmut¹^ORCID,Kampmann Johannes¹

Affiliation:

1. Fakultät für Mathematik , Universität Regensburg , 93040 Regensburg , Germany

Abstract

Abstract We rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed in [H. Garcke, J. Kampmann, A. Rätz and M. Röger, A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes, Math. Models Methods Appl. Sci. 26 2016, 6, 1149–1189] 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 in [X. Chen, Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom. 44 1996, 2, 262–311] for the corresponding result for the Cahn–Hilliard equation.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

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