A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes

DOI10.1142/S0218202516500275zbMath1338.35222MaRDI QIDQ2806549

Matthias Röger, Andreas Rätz, Harald Garcke, Johannes Kampmann

Publication date: 18 May 2016

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

reaction-diffusion systemsCahn-Hilliard equationphase separationsingular limitOhta-Kawasaki energypartial differential equations on surfaces

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell biology (92C37) Moving boundary problems for PDEs (35R37) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items

Numerical modeling of phase separation on dynamic surfaces, Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type, On the sharp interface limit of a phase field model for near spherical two phase biomembranes, On a model for phase separation on biological membranes and its relation to the Ohta–Kawasaki equation, A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation, Derivation and simulation of a two-phase fluid deformable surface model, Existence of weak solutions for a sharp interface model for phase separation on biological membranes, Local changes in lipid composition to match membrane curvature, A finite element method for Allen-Cahn equation on deforming surface, Well-posedness and fast-diffusion limit for a bulk-surface reaction-diffusion system, On the sharp interface limit of a model for phase separation on biological membranes, Cahn-Hilliard equation on the boundary with bulk condition of Allen-Cahn type, On a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition and its approximation by a Robin boundary condition, Domain formation via phase separation for spherical biomembranes with small deformations, A benchmark for the surface Cahn-Hilliard equation

Uses Software

• Maple
• AMDiS

Cites Work

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• Analysis of the Diffuse Domain Approach for a Bulk-Surface Coupled PDE System
• Computation of geometric partial differential equations and mean curvature flow
• On a nonequilibrium thermodynamics of capillarity and phase