The main concern of this article is to deal with the presence of a boundary delay in the nonlinear Kuramoto-Sivashinsky equation. First, we prove that the whole system is well-posed under a smallness assumption on the initial data and a condition on the parameter involved in the delay term. Then, the solution is shown to decay exponentially despite the presence of the delay. These findings are proved by considering several situations depending on the physical parameters of the system.

中文翻译：

---

具有边界时滞的非线性 Kuramoto-Sivashinsky 方程的适定性和指数稳定性结果

本文主要关注的是处理非线性 Kuramoto-Sivashinsky 方程中边界延迟的存在。首先，我们证明整个系统在初始数据的小假设和延迟项中涉及的参数的条件下是适定的。然后，尽管存在延迟，解仍呈指数衰减。通过考虑取决于系统物理参数的几种情况来证明这些发现。