Global solution branches for a nonlocal Allen–Cahn equation

Kousuke Kuto, Tatsuki Mori, Tohru Tsujikawa, Shoji Yotsutani

Research output: Contribution to journalArticle

Abstract

We consider the Neumann problem of a 1D stationary Allen–Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric solutions which bifurcates from a point on the branch of odd-symmetric solutions. This paper derives the global behavior of the branch of asymmetric solutions, and moreover, determines the set of all solutions to the nonlocal Allen–Cahn equation. Our proof is based on a level set analysis for an integral map associated with the nonlocal term.

Original languageEnglish
Pages (from-to)5928-5949
Number of pages22
JournalJournal of Differential Equations
Volume264
Issue number9
DOIs
Publication statusPublished - 2018 May 5
Externally publishedYes

Fingerprint

Allen-Cahn Equation
Nonlocal Equations
Global Solution
Branch
Symmetric Solution
Neumann Problem
Term
Level Set
Odd

Keywords

  • Allen–Cahn equation
  • Bifurcation
  • Level set analysis
  • Monotonicity
  • Nonlocal term

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Global solution branches for a nonlocal Allen–Cahn equation. / Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji.

In: Journal of Differential Equations, Vol. 264, No. 9, 05.05.2018, p. 5928-5949.

Research output: Contribution to journalArticle

Kuto, Kousuke ; Mori, Tatsuki ; Tsujikawa, Tohru ; Yotsutani, Shoji. / Global solution branches for a nonlocal Allen–Cahn equation. In: Journal of Differential Equations. 2018 ; Vol. 264, No. 9. pp. 5928-5949.
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