论文标题
超冷的Stefan问题中的零动力学底座极限
Zero kinetic undercooling limit in the supercooled Stefan problem
论文作者
论文摘要
我们研究了动态过冷的单相超冷的Stefan问题的解决方案，该问题描述了一个空间尺寸的过冷液体的冻结。 Assuming that the initial temperature lies between the equilibrium freezing point and the characteristic invariant temperature throughout the liquid our main theorem shows that, as the kinetic undercooling parameter tends to zero, the free boundary converges to the (possibly irregular) free boundary in the supercooled Stefan problem without kinetic undercooling, whose uniqueness has been recently established in [DNS19], [LS18b].证明中的关键工具是Feynman-KAC公式，它通过反射过程的本地时间进行过冷的问题表达了自由边界，以及具有不同动力学底层底层底层参数的自由边界的结果比较原理。
We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium freezing point and the characteristic invariant temperature throughout the liquid our main theorem shows that, as the kinetic undercooling parameter tends to zero, the free boundary converges to the (possibly irregular) free boundary in the supercooled Stefan problem without kinetic undercooling, whose uniqueness has been recently established in [DNS19], [LS18b]. The key tools in the proof are a Feynman-Kac formula, which expresses the free boundary in the problem with kinetic undercooling through a local time of a reflected process, and a resulting comparison principle for the free boundaries with different kinetic undercooling parameters.
