Secondary bifurcation for a nonlocal Allen–Cahn equation

Kousuke Kuto, Tatsuki Mori, Tohru Tsujikawa, Shoji Yotsutani

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper studies the Neumann problem of a nonlocal Allen–Cahn equation in an interval. A main result finds a symmetry breaking (secondary) bifurcation point on the bifurcation curve of solutions with odd-symmetry. Our proof is based on a level set analysis for the associated integral map. A method using the complete elliptic integrals proves the uniqueness of secondary bifurcation point. We also show some numerical simulations concerning the global bifurcation structure.

Original languageEnglish
Pages (from-to)2687-2714
Number of pages28
JournalJournal of Differential Equations
Volume263
Issue number5
DOIs
Publication statusPublished - 2017 Sep 5

Keywords

  • Allen–Cahn equation
  • Bifurcation
  • Complete elliptic integrals
  • Nonlocal term
  • Symmetry breaking

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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