Existence and global stability of traveling curved fronts in the Allen-Cahn equations
Existence and global stability of traveling curved fronts in the Allen-Cahn equations
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DOI：
10.1016/j.jde.2004.06.011
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发表时间：
2005-06
影响因子：
2.4
通讯作者：
H. Ninomiya;M. Taniguchi
中科院分区：
文献类型：
--
作者：
H. Ninomiya;M. Taniguchi
本文关注的是二维空间中 Allen-Cahn 方程的行进曲锋的存在性和稳定性。利用超解和子解构造了行波曲锋，并证明它是它们之间唯一的行波解。我们的超解可以取任意大，这意味着行进的弯曲锋面具有一定的全局渐近稳定性。
This paper is concerned with existence and stability of traveling curved fronts for the Allen–Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front.