Convergence of phase-field approximations to the Gibbs–Thomson law

• Röger, Matthias

• Tonegawa, Yoshihiro

抄録

We prove the convergence of phase-field approximations of the Gibbs–Thomson law. This establishes a relation between the first variation of the Van-der-Waals–Cahn–Hilliard energy and the first variation of the area functional. We allow for folding of diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the multiplicity does not affect the Gibbs–Thomson law and that the mean curvature vanishes where diffuse interfaces have collided. We apply our results to prove the convergence of stationary points of the Cahn–Hilliard equation to constant mean curvature surfaces and the convergence of stationary points of an energy functional that was proposed by Ohta–Kawasaki as a model for micro-phase separation in block-copolymers.

収録刊行物

• Calculus of Variations and Partial Differential Equations

  Calculus of Variations and Partial Differential Equations 32 (1), 111-136, 2008-05

  Springer Berlin / Heidelberg

詳細情報

• CRID: 1050564288948655872
• NII論文ID: 120000952615
• NII書誌ID: AA10848617
• ISSN: 14320835
• ISSN: 09442669
• HANDLE: 2115/33792
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles
  • KAKEN