论文标题
具有强烈不可逆性的艾伦-CAHN方程的行驶波动力学
Traveling wave dynamics for Allen-Cahn equations with strong irreversibility
论文作者
论文摘要
在断裂力学中研究了受限的梯度流，以描述裂纹的强烈不可逆（或单向）演变。本文致力于研究这种约束梯度流的非紧凑轨道的长期行为。更确切地说，考虑到涉及正聚合函数的一维完全非线性allen-cahn类型方程的行驶波动力学。本文的主要结果包括构造单参数的退化波动波解决方案家族（甚至在翻译时都确定）以及这种行进波解决方案具有一些吸引力的盆地的指数稳定性，尽管它们在通常的含义上是不稳定的。
Constrained gradient flows are studied in fracture mechanics to describe strongly irreversible (or unidirectional) evolution of cracks. The present paper is devoted to a study on the long-time behavior of non-compact orbits of such constrained gradient flows. More precisely, traveling wave dynamics for a one-dimensional fully nonlinear Allen-Cahn type equation involving the positive-part function is considered. Main results of the paper consist of a construction of a one-parameter family of degenerate traveling wave solutions (even identified when coinciding up to translation) and exponential stability of such traveling wave solutions with some basin of attraction, although they are unstable in a usual sense.
