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

  • * Corresponding author: Helmut Abels

    * Corresponding author: Helmut Abels 
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  • 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.

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  • [1] H. Abels and J. Kampmann, On the sharp interface limit of a model for phase separation on biological membranes, Preprint, arXiv: 1811.12489, 2018.
    [2] H. Abels and M. Röger, Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 2403-2424.  doi: 10.1016/j.anihpc.2009.06.002.
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    [5] H. GarckeJ. KampmannA. 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), 1149-1189.  doi: 10.1142/S0218202516500275.
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