Article Contents
Article Contents

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

• * Corresponding author: Helmut Abels
• 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.

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

 Citation:

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