接触线摩擦下的液滴运动：完全润湿情形下的长时间渐近行为
Droplet motion with contact-line friction: long-time asymptotics in complete wetting
AI总结：
本文研究完全润湿情形下带接触线摩擦的薄液膜方程，利用准自相似解刻画液滴铺展速率与轮廓的长时间渐近行为，并结合瞬态数值解验证理论结果。
摘要：
我们考虑由 E 和 Ren 引入的一类模拟接触线摩擦的自由边界条件下的薄液膜方程。本文的分析重点在于完全润湿状态下解的长时间渐近行为。特别地，通过分析准自相似解，我们刻画了依赖于接触线摩擦强度的解的轮廓和铺展速率，以及由自由边界条件的动力学性质所导致的（全局或局部）修正。这些结果辅以自由边界问题的完整瞬态数值解。
英文摘要：
We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particular, through the analysis of quasi-self-similar solutions, we characterize the profile and the spreading rate of solutions depending on the strength of friction at the contact line, as well as their (global or local) corrections, which are due to the dynamical nature of the free boundary conditions. These results are complemented with full transient numerical solutions of the free boundary problem.
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