SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1944-1957, January 2021.
We prove an observability inequality from two time points for the linear KdV equation with an explicit constant. The proof relies on a quantitative analytic estimate for the linear KdV with compact support initial data and an uncertainty principle of super-analytic functions. Moreover, we obtain similar unique continuation inequalities for gKdV equations by our linear results and an energy induction strategy. Both results can be seen as a quantitative characterization of unique continuation properties.

中文翻译：

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KdV方程在两个时间点的可观测性不等式

SIAM数学分析杂志，第53卷，第2期，第1944-1957页，2021年1月。
我们证明了线性KdV方程具有显式常数的两个时间点的可观测性不等式。证明依赖于具有紧凑支持初始数据和超解析函数的不确定性原理的线性KdV的定量分析估计。此外，通过我们的线性结果和能量感应策略，我们获得了gKdV方程的相似唯一连续不等式。两种结果都可以看作是对独特连续性的定量表征。