Secondary bifurcation for a nonlocal Allen–Cahn equation

Kousuke Kuto, Tatsuki Mori, Tohru Tsujikawa, Shoji Yotsutani

研究成果: Article

3 引用 (Scopus)

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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.

元の言語English
ページ(範囲)2687-2714
ページ数28
ジャーナルJournal of Differential Equations
263
発行部数5
DOI
出版物ステータスPublished - 2017 9 5
外部発表Yes

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ASJC Scopus subject areas

  • Analysis

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