Mathematical analysis related to a model of droplet motion

建立了包括接触角动力学在内的液滴表面运动模型，并对该问题进行了数学分析。发现接触角的演变取决于液滴表面的运动模式，并针对两种基本运动模式导出了相应问题解的一些性质。此外，本文还介绍了一种难以用数学方法处理的带有连接的多界面问题的数值逼近方法，并表明该方法具有推广应用于数学分析的前景。

A model was developed for the motion of droplets on surfaces including the dynamics of contact angle, and mathematical analysis of the problem was performed. It was found that the evolution of the contact angle depends on the mode of motion of the droplet surface, and for two basic modes of motion some of the properties of solutions to the corresponding problem were derived. Moreover, a numerical approximation method was introduced for the problem of several interfaces with junctions, which has been considered as difficult to treat mathematically, and it was shown that the suggested method has a perspective to be extended as a tool of mathematical analysis.