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CONVERGENCE OF PHASE–FIELD APPROXIMATIONS TO THE GIBBS–THOMSON LAW
| Title: | CONVERGENCE OF PHASE–FIELD APPROXIMATIONS TO THE GIBBS–THOMSON LAW |
| Authors: | ROGER, MATTHIAS Browse this author | | TONEGAWA, YOSHIHIRO Browse this author |
| Keywords: | Phase Transitions | | Geometric Measure Theory | | Singular Perturbations | | Cahn–Hilliard Energy | | Gibbs–Thomson Law | | Block-copolymers |
| Issue Date: | 2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 840 |
| Start Page: | 1 |
| End Page: | 25 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69649 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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