| Abstract: |
| In this talk, we will present a phase-field model for curvature-driven pattern formation in biomembranes. The model is obtained as a gradient flow of an energy that approximates the two-phase Canham--Helfrich functional, which leads to a Cahn--Hilliard-type equation with cross diffusion for the lipid concentration, coupled to a fourth-order equation for the membrane
height. We establish existence and uniqueness of weak solutions for this system, both for regular and for singular potentials. In addition, we present numerical simulations that demonstrate how different parameter regimes give rise to striped, dotted, or snake-like patterns on the membrane. The talk is based on a joint work with Patrik Knopf and Dennis Trautwein. |
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