Convergence of phase-field approximations to the Gibbs–Thomson law
スポンサーリンク
概要
- 論文の詳細を見る
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.
- Springer Berlin / Heidelbergの論文
著者
-
利根川 吉広
北海道大学理学院
-
Tonegawa Yoshihiro
Department Of Mathematics Hokkaido University
-
Tonegawa Yoshihiro
Department Of Mathematics Faculty Of Science Hokkaido University
関連論文
- ON THE TIME-GLOBAL EXISTENCE FOR NON-NEWTONIAN TOW-PHASE FLOW WITH DIFFERENT DENSITIES (Mathematical Analysis in Fluid and Gas Dynamics)
- A new two-phase fluid problem with surface energy (Progress in Variational Problems : New Trends of Geometric Gradient Flow and Critical Point Theory)
- Proceedings of the 30th Sapporo Symposium on Partial Differential Equations
- Proceedings of the 29th Sapporo Symposium on Partial Differential Equations
- 2相分離問題への幾何学的測度論の応用
- フェイズフィールド法の数学、入門と概説(非線形数理 冬の学校,講義ノート)
- Interior gradient estimate for curvature flow (Variational Problems and Related Topics 研究集会報告集)
- Note on the small-scale structure of the phase boundaries (Viscosity Solutions of Differential Equations and Related Topics)
- 2相場の特異摂動問題について (変分問題とその周辺)
- MATHEMATICAL ANALYSIS OF TWO-PHASE FIELD MODEL WITH SURFACE TENSION EFFECT (Nonlinear Diffusive Systems : Dynamics and Asymptotics)
- A singular perturbation problem with integral curvature bound
- NOTE ON THE MODICA-MORTOLA FUNCTIONAL(Viscosity Solution Theory of Differential Equations and its Developments)
- Convergence of phase-field approximations to the Gibbs–Thomson law
- Integrality of varifolds in the singular limit of reaction-diffusion equations