Existence of weak solutions for a sharp interface model for phase separation on biological membranes
2018
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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