论文标题
Kawahara方程的两个稳定性结果，具有时间延迟的边界控制
Two stability results for the Kawahara equation with a time-delayed boundary control
论文作者
论文摘要
在本文中，我们以界面的间隔考虑了川毛方程，并在一个边界条件下具有延迟项。使用两种不同的方法，我们证明该系统在空间域的长度上的条件下呈指数稳定。具体而言，第一个结果是通过引入合适的能量和使用Lyapunov方法来获得的，以确保Kawahara系统的独特解决方案呈指数衰减。第二个结果是通过紧凑的唯一性论证来实现的，这减少了我们的研究以证明可观察到的不平等。此外，这项工作的主要新颖性是通过表明每当空间长度与Möbius变换相关时，表征该方程的关键集合现象。
In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the length of the spatial domain. Specifically, the first result is obtained by introducing a suitable energy and using the Lyapunov approach, to ensure that the unique solution of the Kawahara system exponentially decays. The second result is achieved by means of a compactness-uniqueness argument, which reduces our study to prove an observability inequality. Furthermore, the main novelty of this work is to characterize the critical set phenomenon for this equation by showing that the stability results hold whenever the spatial length is related to the Möbius transformations.
