{
  "id": "2012.12580",
  "version": "v1",
  "published": "2020-12-23T10:11:39.000Z",
  "updated": "2020-12-23T10:11:39.000Z",
  "title": "On the sharp interface limit of a phase field model for near-spherical two phase biomembranes",
  "authors": [
    "Charles M. Elliott",
    "Luke Hatcher",
    "Björn Stinner"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is motivated by lipid raft formation. We introduce a reduced diffuse interface energy depending only on the membrane composition and derive the $\\Gamma-$limit. We demonstrate 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-23T10:11:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase field model",
      "sharp interface limit",
      "pde free boundary problem",
      "order pde free boundary",
      "phase biomembranes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}