Zero kinetic undercooling limit in the supercooled Stefan problem
Zero kinetic undercooling limit in the supercooled Stefan problem
复制标题
过冷 Stefan 问题中的零动力学过冷极限
DOI：
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发表时间：
2020
影响因子：
1.5
通讯作者：
Mykhaylo Shkolnikov
中科院分区：
文献类型：
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作者：
G. Baker;Mykhaylo Shkolnikov
研究了具有动力学过冷的单相过冷Stefan问题的一维解，该问题描述了过冷液体的冻结过程。假设初始温度介于整个液体的平衡凝固点和特征不变温度之间，我们的主要定理表明，当动力学过冷参数趋于零时，自由边界收敛于无动力学过冷的过冷Stefan问题（可能是不规则的）自由边界，其唯一性已在[DNS19]， [LS18b]中得到证实。证明的关键工具是费曼-卡茨公式，该公式通过反射过程的局部时间来表示动力学过冷问题的自由边界，并由此得出不同动力学过冷参数下自由边界的比较原理。
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.
DOI：
10.2140/pmp.2022.3.171
发表时间：
2019-02
期刊：
Probability and Mathematical Physics
影响因子：
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作者：
F. Delarue;S. Nadtochiy;Mykhaylo Shkolnikov
通讯作者：
F. Delarue;S. Nadtochiy;Mykhaylo Shkolnikov