Interface foliation for an inhomogeneous Allen–Cahn equation in Riemannian manifolds
Interface foliation for an inhomogeneous Allen–Cahn equation in Riemannian manifolds
复制标题
DOI：
10.1007/s00526-012-0521-4
复制
发表时间：
2013-05
影响因子：
2.1
通讯作者：
Zhuoran Du;Liping Wang
中科院分区：
文献类型：
--
作者：
Zhuoran Du;Liping Wang
设是一个N维光滑紧黎曼流形。本文考虑了一个小参数，V是正的光滑函数的问题。设是一个（N-1）维光滑子流形，它分成两个不相交的分支。我们假设κ相对于加权面积泛函是平稳的和非退化的。对于任意≥ 2的整数，证明了在k附近存在一个m过渡层的序列和两个方向相反的解，它们之间的距离为.此外，相邻层之间的相互作用由一类Jacobi-Toda系统控制。
Letbe anN-dimensional smooth compact Riemannian manifold. We consider the problem, whereis a small parameter andVis a positive, smooth function in. Letbe an (N− 1)-dimensional smooth submanifold that dividesinto two disjoint components. We assumeκis stationary and non-degenerate relative to the weighted area functional. For each integerm≥ 2, we prove the existence of a sequence, and two opposite directional solutions withm-transition layers nearκ, whose mutual distance is. Moreover, the interaction between neighboring layers is governed by a type of Jacobi–Toda system.