论文标题
被动和主动艾伦 - 卡恩型方程中前运动的分叉
Bifurcations of front motion in passive and active Allen-Cahn-type equations
论文作者
论文摘要
众所周知的立方体Allen-CAHN（AC）方程是一个简单的梯度动力学（或变异）模型，用于未经保守的顺序参数字段。在修改了不同类型的移动前部的主要文献结果之后，我们采用路径延续来确定其分叉图，以依赖外部野外强度或化学潜力。然后，我们采用相同的方法来系统地分析更多涉及的AC-Type模型。特别是，我们考虑了一个立方敏感的变异AC模型和两个不同的非变化概括。我们确定并比较四个被考虑的模型中前溶液的分叉图。
The well-known cubic Allen-Cahn (AC) equation is a simple gradient dynamics (or variational) model for a nonconserved order parameter field. After revising main literature results for the occuring different types of moving fronts, we employ path continuation to determine their bifurcation diagram in dependence of the external field strength or chemical potential. We then employ the same methodology to systematically analyse fronts for more involved AC-type models. In particular, we consider a cubic-quintic variational AC model and two different nonvariational generalisations. We determine and compare the bifurcation diagrams of front solutions in the four considered models.
