Analytic smoothing estimates for the Korteweg-de Vries equation with steplike data
Analytic smoothing estimates for the Korteweg-de Vries equation with steplike data
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具有阶梯数据的 Korteweg-de Vries 方程的解析平滑估计
DOI：
10.1088/1361-6544/abfd78
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发表时间：
2021
期刊：
影响因子：
1.7
通讯作者：
Ze Li
中科院分区：
文献类型：
--
作者：
Ze Li
本文证明了Korteweg-de弗里斯方程的解析光滑估计。在第一个结果中，我们得到了显式的解析光滑估计的初始数据在Faddeev类的指数衰减的正方向。在第二个结果中，我们超越了Faddeev类，并将结果推广到非衰减的初始数据。特别地，第二个结果涉及左半线上的阶跃函数及其由正指数衰减的Faddeev类势扰动。最后，我们讨论了它的一些应用控制问题，如KdV方程的可观测性不等式。
In this paper, we prove analytic smoothing estimates for the Korteweg–de Vries equation. In the first result, we obtain explicit analytic smoothing estimates for initial data in Faddeev class which decays exponentially in the positive direction. In the second result, we go beyond Faddeev class and generalize the result to non-decaying initial data. Particularly, step functions supported in the left half line and their perturbations by Faddeev class potentials decaying exponentially in positive direction are involved by the second result. Finally, we discuss some of its applications to control problems such as observability inequalities for the KdV equation.