Secondary bifurcation for a nonlocal Allen-Cahn equation

被引：8
|
作者：
Kuto, Kousuke [1 ]
Mori, Tatsuki [2 ]
Tsujikawa, Tohru [3 ]
Yotsutani, Shoji [4 ]
机构：
[1] Univ Electrocommun, Dept Commun Engn & Informat, Chofu, Tokyo 1828585, Japan
[2] Osaka Univ, Grad Sch Engn Sci, Toyonaka, Osaka 5608531, Japan
[3] Univ Miyazaki, Fac Engn, Miyazaki 8892192, Japan
[4] Ryukoku Univ, Dept Appl Math & Informat, Otsu, Shiga 5202194, Japan
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 05期
关键词：
Allen-Cahn equation; Nonlocal term; Bifurcation; Symmetry breaking; Complete elliptic integrals; CELL POLARIZATION; DIFFUSION; MODEL; EIGENVALUES;
D O I：
10.1016/j.jde.2017.04.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：2687 / 2714
页数：28
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