CONVERGENCE OF THE ALLEN-CAHN EQUATION WITH NEUMANN BOUNDARY CONDITIONS

• Mizuno Masashi

• Tonegawa Yoshihiro

Abstract

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke’s mean curvature flow with a gen- eralized right angle condition on the boundary.

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 1057 1-26, 2014-06-09

  Department of Mathematics, Hokkaido University

Keywords

• Boundary monotonicity formula
• Allen-Cahn equation
• mean curvature flow
• varifold

Details

• CRID: 1390009224795467392
• NII Article ID: 120006459746
• DOI: 10.14943/84201
• HANDLE: 2115/69861
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed