曲阜师范大学学报（自然科学版）2019，Vol.45Issue(2)：15-26,12.DOI:10.3969/j.issn.1001-5337.2019.2.015
平面上变系数Allen-Cahn方程的multiple-end解
Multiple-end solutions of the variable coefficient Allen-Cahn equation on the plane
刘旋1
作者信息
- 1. 华北电力大学数理学院,102206,北京市
- 折叠
摘要
Abstract
The Allen-Cahn equation has multiple-end solutions on the plane,we construct a similar class of entire solutions for the variable coefficient Allen-Cahn equation for further study.Given k ≥ 1,we can find a family of solutions whose zero level sets are,away from a compact set,asymptotic to 2k straight lines (which are called the ends).These solutions have the property that limr→+∞ u(reiθ) =(-1)j uniformly in θ on compact subsets of (θj,θj+1)when there exist θ0 ＜ θ1 ＜ … ＜ θ2k =θ0 +2π,forj =0,…,2k-1.关键词
二维变系数/Allen-Cahn方程/Toda系统/multiple-end解/Lyapunov-Schmidt还原论证法Key words
variable coefficient/Allen-Cahn equation/Toda system/multiple-end solutions/Lyapunov-Schmidt reduction分类
数理科学引用本文复制引用
刘旋..平面上变系数Allen-Cahn方程的multiple-end解[J].曲阜师范大学学报（自然科学版）,2019,45(2):15-26,12.
