文章基本信息

标题：Periodic solutions for the Allen-Cahn equation
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作者：Rui Huang ; Haochuan Huang ; Shanming Ji 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：295
DOI：10.1186/s13662-015-0631-3
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper we consider the time-periodic Allen-Cahn equation subject to homogeneous boundary value condition and time-periodic condition. For the case of a smooth bounded domain with spatial dimension N ≤ 3 $N\leq 3$ , we prove the existence of classical nontrivial periodic solutions. For the case of a star shaped domain with N ≥ 4 $N\geq4$ , we prove the nonexistence of nontrivial periodic solutions. For the case of an annulus domain with N ≥ 3 $N \geq3 $ , we prove the existence of nontrivial radial periodic solutions. Some numerical simulations are also presented to illustrate our results.
关键词：periodic solutions ; existence ; nonexistence ; numerical simulations