Abstract: |
We investigate a model for lipid raft formation and dynamics in biological membranes which
was proposed by Garcke, Kampmann, R\atz and R\oger. The model includes an cholesterol exchange between cytosol and cell membrane and takes lipid-cholesterol interaction energy into account. This leads to a diffusion equation in the bulk coupled to a Cahn-Hilliard type equation on the surface that describes the membrane. In particular, the
evolution on the surface describes a relaxation dynamics for an energy which includes lipid-phase separation
and lipid-cholesterol interaction energy. In dependence on the constitutive laws for the exchange
between cell membrane and cytosol, the resulting model can include nonequilibrium processes.
We discuss mathematical properties of the model and a connection to the Ohta-Kawasaki equation
by showing that weak solutions to this model converge to the solutions to the Ohta-Kawasaki
equation if certain parameters in the model tend to zero. |
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