On a thin film model with insoluble surfactant

一类退化抛物型方程组的整体弱解

Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant

证明了一类退化抛物方程组非负弱解的整体存在性，该方程组描述了不溶性表面活性剂在薄液膜上的扩散。

重力和不溶性表面活性剂作用下薄膜的有界行波

Bounded traveling waves for a thin film with gravity and insoluble surfactant

考虑了表面张力依赖于表面张力的薄层流体表面张力驱动流动的润滑方程。结果表明，存在一个有界行波解，它连接一个完全表面涂覆的膜到一个未涂覆的膜。行波的规则性取决于是否包括不溶性表面活性剂的表面扩散。

具有毛细管效应和不溶性表面活性剂的薄膜模型的弱解

Weak solutions to a thin film model with capillary effects and insoluble surfactant

本文重点介绍了一个模型，描述了不溶性表面活性剂的蔓延薄粘性膜的毛细效应考虑。液膜高度的控制方程为四阶退化抛物方程，并与表面活性剂浓度的二阶抛物型方程耦合。结果表明，非负的弱解存在自然假设的表面张力系数。

Weak solutions to a two-phase thin film model with insoluble surfactant driven by capillary effects

Of concern is the study of a system of three equations describing the motion of a viscous complete wetting two-phase thin film endowed with a layer of insoluble surfactant on the surface of the upper fluid under the effects of capillary forces. The governing equations for the film heights of the two-phase flow are degenerate, parabolic and strongly coupled fourth-order equations, which are additionally coupled to a second-order parabolic transport equation for the surfactant concentration. A result on the existence of non-negative global weak solutions is presented.

Modeling and Analysis of a Two-Phase Thin Film Model with Insoluble Surfactant

In this paper we consider a two-phase thin film consisting of two immiscible viscous fluids endowed with a layer of insoluble surfactant on the surface of the upper fluid. The governing equations for the two film heights and the surfactant concentration are derived using a lubrication approximation. Taking gravitational forces into account but neglecting capillary effects, the resulting system of evolution equations is parabolic, strongly coupled, of second order and degenerated in the equations for the two film heights. Incorporating on the contrary capillary forces and neglecting the effects…

Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant…