Secondary bifurcation for a nonlocal Allen–Cahn equation

Kousuke Kuto; Tatsuki Mori; Tohru Tsujikawa; Shoji Yotsutani

doi:10.1016/j.jde.2017.04.010

Secondary bifurcation for a nonlocal Allen–Cahn equation

Kousuke Kuto^*, Tatsuki Mori, Tohru Tsujikawa, Shoji Yotsutani

^*この研究の対応する著者

研究成果: Article › 査読

6 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	2687-2714
ページ数	28
ジャーナル	Journal of Differential Equations
巻	263
号	5
DOI	https://doi.org/10.1016/j.jde.2017.04.010
出版ステータス	Published - 2017 9月 5
外部発表	はい

ASJC Scopus subject areas

分析
応用数学

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10.1016/j.jde.2017.04.010

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title = "Secondary bifurcation for a nonlocal Allen–Cahn equation",

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.",

keywords = "Allen–Cahn equation, Bifurcation, Complete elliptic integrals, Nonlocal term, Symmetry breaking",

author = "Kousuke Kuto and Tatsuki Mori and Tohru Tsujikawa and Shoji Yotsutani",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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T1 - Secondary bifurcation for a nonlocal Allen–Cahn equation

AU - Kuto, Kousuke

AU - Mori, Tatsuki

AU - Tsujikawa, Tohru

AU - Yotsutani, Shoji

PY - 2017/9/5

Y1 - 2017/9/5

N2 - 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.

AB - 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.

KW - Allen–Cahn equation

KW - Bifurcation

KW - Complete elliptic integrals

KW - Nonlocal term

KW - Symmetry breaking

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DO - 10.1016/j.jde.2017.04.010

M3 - Article

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SN - 0022-0396

VL - 263

SP - 2687

EP - 2714

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

Secondary bifurcation for a nonlocal Allen–Cahn equation

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