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 during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap. Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable.

中文翻译：

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表面活性剂薄膜方程中混合阶系统的适定性和稳定性

本工作的目的是为具有不溶性表面活性剂的毛细管驱动薄膜方程提供适定结果。由此产生的演化方程抛物线系统不仅是强耦合和退化的，而且是混合阶的。据我们所知，同一作者在 [4] 中提供了具有表面活性剂的毛细管驱动薄膜的唯一适定结果，其中假设表面活性剂浓度的严重小条件来证明结果。因此，尽管在过去十年中对表面活性剂的薄膜方程进行了深入的分析研究，但文献中仍然缺少适当的适定性结果。本文旨在填补这一空白。此外，