An (N-1)-dimensional convex compact set gives an N-dimensional traveling front in the Allen--Cahn equation

• Taniguchi, Masaharu

Bibliographic Information

Other Title

• An (N−1)-dimensional convex compact set gives an N-dimensional traveling front in the Allen–Cahn equation

Abstract

This paper studies traveling fronts to the Allen–Cahn equation in RN for N ≥ 3. Let (N −2)-dimensional smooth surfaces be the boundaries of compact sets in RN−1 and assume that all principal curvatures are positive everywhere. We define an equivalence relation between them and prove that there exists a traveling front associated with a given surface and that it is asymptotically stable for given initial perturbation. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.

Journal

• SIAM Journal on Mathematical Analysis

  SIAM Journal on Mathematical Analysis 47 (1), 455-476, 2015-01

  Society for Industrial and Applied Mathematics

Keywords

• traveling front
• Allen–Cahn equation
• nonsymmetric

Details

• CRID: 1050565162289498880
• NII Article ID: 120005657667
• NII Book ID: AA00424217
• ISSN: 00361410
• ISSN: 10957154
• DOI: 10.1137/130945041
• Web Site: https://ousar.lib.okayama-u.ac.jp/53604
• Web Site: http://epubs.siam.org/doi/pdf/10.1137/130945041
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN