Existence of weak solutions for a sharp interface model for phase separation on biological membranes

Helmut Abels; Johannes Kampmann

doi:10.3934/dcdss.2020325

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2021, Volume 14, Issue 1: 331-351. Doi: 10.3934/dcdss.2020325

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Existence of weak solutions for a sharp interface model for phase separation on biological membranes

Helmut Abels^, and
Johannes Kampmann

Faculty of Mathematics, University of Regensburg, 93040 Regensburg, Germany

^* Corresponding author: Helmut Abels
^* Corresponding author: Helmut Abels

Received: February 28, 2019

Revised: August 31, 2019

Early access: April 2020

Published: January 2021

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Abstract

We prove existence of weak solutions of a Mullins-Sekerka equation on a surface that is coupled to diffusion equations in a bulk domain and on the boundary. This model arises as a sharp interface limit of a phase field model to describe the formation of liqid rafts on a cell membrane. The solutions are constructed with the aid of an implicit time discretization and tools from geometric measure theory to pass to the limit.

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Mathematics Subject Classification: Primary: 35R35; Secondary: 35K93, 92C37.

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References

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