被动和主动Allen-Cahn型方程的锋运动分支
Bifurcations of front motion in passive and active Allen-Cahn-type equations
摘要：
著名的三次Allen-Cahn（AC）方程是非守恒序参量场的简单梯度动力学（或变分）模型。在修正了主要文献结果后，我们采用路径延拓方法确定了它们的分岔图，并将其与外场强度或化学势的关系进行了比较。然后，我们采用相同的方法来系统地分析更多涉及AC型模型的前沿。特别地，我们考虑了一个五次变分AC模型和两个不同的非变分推广。我们确定并比较了四个模型的前沿解的分歧图。
英文摘要：
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.
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