Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains
Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains
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DOI：
10.3934/dcds.2012.32.1391
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发表时间：
2011-10
影响因子：
1.1
通讯作者：
Fang Li;K. Nakashima
中科院分区：
文献类型：
--
作者：
Fang Li;K. Nakashima
本文研究了多维区域上的空间非齐次Allen-Cahn方程。利用上下解方法，得到了域$\Omega$中的超曲面$S$支持稳定过渡层的充分条件，以及域$\Omega$中的超曲面$S$支持过渡层但不一定稳定的必要条件.此外，还得到了过渡层深度的精确估计。
In this paper, we study a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains. By upper and lower solution method, we obtain a sufficient condition for a hypersurface $S$ in the domain $\Omega$ to support stable transition layers, and a necessary condition for $S$ in $\Omega$ to support transition layers, not necessarily stable. In addition, sharp estimates on depths of transition layers have also been derived.