标题： 粒子系统与非可积初始数据的过冷Stefan问题 显示英文标题

标题： Particle systems and the supercooled Stefan problem with non-integrable initial data

摘要： 我们考虑一个在正实线上无限的粒子系统，初始状态为泊松点过程，这些粒子按照布朗运动移动，直到碰到障碍物的时间。 当障碍物被碰到时，障碍物会增加，从而允许连续跳跃序列同时发生。 在某些条件下，缩放极限给出了过冷 Stefan 问题及其自由边界的一个表示。 这使我们能够给出障碍物的精确渐近极限并确定收敛速率，解决了 arXiv:1112.6257 中的一个猜想。 从这个表示中，我们还研究了初始数据不在$L^1(\mathbb{R}^+)$中时的过冷 Stefan 问题的性质。 在临界情况下，当跳跃大小与泊松过程的密度相匹配且 Stefan 问题出现瞬时爆炸时，我们则恢复了与 arXiv:1705.10017 中相同的缩放极限结果。 显示英文摘要

摘要： We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing for the possibility of sequences of successive jumps to occur instantaneously. Under certain conditions, the scaling limit gives a representation for the supercooled Stefan problem and its free boundary. This allows us to give a precise asymptotic limit for the barrier and determine the rate of convergence, resolving a conjecture of arXiv:1112.6257. From this representation, we also investigate properties of the supercooled Stefan problem for initial data not in $L^1(\mathbb{R}^+)$. In a critical case, where the jump size matches the density of the Poisson process and the Stefan problem has an instantaneous explosion, we instead recover the same scaling limit result as in arXiv:1705.10017.