| Abstract: |
| In this talk, we study the quantitative exponential stability of the KdV equation on a finite interval, focusing on the cases where the length is close to the critical set. Through a constructive PDE control framework, we obtain sharp decay estimates for such cases. Specifically, I will introduce a transition-stabilization approach that combines the Lebeau--Robbiano strategy with the moment method to establish quantitative null controllability for the KdV equation. Furthermore, based on a classification of these critical lengths, we show that the KdV equation exhibits different asymptotic behaviors near different types of critical lengths. This is a joint work with Shengquan Xiang. |
|