Representation formulas of solutions and bifurcation sheets to a nonlocal allen-cahn equation

Tatsuki Mori, Kousuke Kuto, Tohru Tsujikawa, Shoji Yotsutani

Research output: Contribution to journalArticle

Abstract

We are interested in the Neumann problem of a 1D stationary Allen-Cahn equation with a nonlocal term. In our previous papers [4] and [5], we obtained a global bifurcation branch, and showed the existence and uniqueness of secondary bifurcation point. At this point, asymmetric solutions bifurcate from a branch of odd-symmetric solutions. In this paper, we give representation formulas of all solutions on the secondary bifurcation branch, and a bifurcation sheet which consists of bifurcation curves with heights.

Original languageEnglish
Pages (from-to)4907-4925
Number of pages19
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume40
Issue number8
DOIs
Publication statusPublished - 2020 Aug

Keywords

  • Allen-Cahn equation
  • Exact solution
  • Nonlocal term

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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