Geodesic
On the sharp interface limit of a phase field model for near spherical two phase biomembranes
Charles M. Elliott1 orcid ; Luke Hatcher1 ; Björn Stinner1
1University of Warwick, Coventry, UK
Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 263-286

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DOI

We consider sharp interface asymptotics for a phase field model motivated by lipid raft formation on near spherical biomembranes involving a coupling between the local mean curvature and the local composition. A reduced diffuse interface energy depending only on the membrane composition is introduced and a Γ-limit is derived. It is shown that the Euler–Lagrange equations for the limiting functional and the sharp interface energy coincide. Finally, we consider a system of gradient flow equations with conserved Allen–Cahn dynamics for the phase field model. Performing a formal asymptotic analysis, we obtain a system of gradient flow equations for the sharp interface energy coupling geodesic curvature flow for the phase interface to a fourth order PDE free boundary problem for the surface deformation.
DOI : 10.4171/ifb/473
Classification : 35-XX, 49-XX
Mots-clés : Phase field, Helfrich, biomembranes, Allen–Cahn and curvature motion

Charles M. Elliott  1   ; Luke Hatcher  1   ; Björn Stinner  1

1 University of Warwick, Coventry, UK 
Charles M. Elliott; Luke Hatcher; Björn Stinner. On the sharp interface limit of a phase field model for near spherical two phase biomembranes. Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 263-286. doi: 10.4171/ifb/473
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     title = {On the sharp interface limit of a phase field model for near spherical two phase biomembranes},
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     year = {2022},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/473/}
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