Water drops on generic Lipschitz continuous surfaces in the sense of differential inclusion solutions

摘要

In this paper, the classical phenomenon of water drops on surfaces is investigated from a mathematical analysis point of view, where the surfaces are extended to generic Lipschitz continuous surfaces instead of smooth ones in the state space. According to the possible nonsmoothness of the surfaces, the problem of solution motions of the system is further discussed in an uniform framework of Filippov differential inclusion obtained from the original differential equation. The motion of the water drops with respect to generic Lipschitz surfaces as well as the equilibrium points on the surface is analyzed and some numerical examples are presented to illustrate the validity of the analysis.