标题： 保持可积性的拉普拉斯增长正则化 显示英文标题

标题： Integrability-preserving regularizations of Laplacian Growth

摘要： 拉普拉斯生长（LG）模型被公认为二维中无尺度聚集模型的一个普遍类，其特征是经典可积性并具有有限时间边界奇点形成。一个离散对应物，扩散限制聚集（或DLA），具有类似的局部生长定律，但具有显著不同的全局行为。对于LG和DLA，目前尚无对长时间解的标度性质的适当描述。在本说明中，我们概述了一种可能的方法，以找到产生正则化LG及其与DLA关系的正确理论。 显示英文摘要

摘要： The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA.