含可溶性表面活性剂和重力的薄膜方程：建模和定态稳定性
Thin Film Equations with Soluble Surfactant and Gravity: Modeling and Stability of Steady States
摘要：
被认为是一个薄膜上的水平固体基板和涂有可溶性表面活性剂。当考虑重力时，使用润滑近似推导出用于膜高度和表面活性剂在表面上和在体中的浓度的控制退化抛物方程。结果表明，定态是渐近稳定的。
英文摘要：
A thin film on a horizontal solid substrate and coated with a soluble surfactant is considered. The governing degenerate parabolic equations for the film height and the surfactant concentrations on the surface and in the bulk are derived using a lubrication approximation when gravity is taken into account. It is shown that the steady states are asymptotically stable.
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