Stability of a Korteweg--de Vries equation close to critical lengths
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914429962027008 |
|---|---|
| author | Niu, Jingrui Xiang, Shengquan |
| author_facet | Niu, Jingrui Xiang, Shengquan |
| contents | In this paper, we investigate the quantitative exponential stability of the Korteweg-de Vries equation on a finite interval with its length close to the critical set. Sharp decay estimates are obtained via a constructive PDE control framework. We first introduce a novel transition-stabilization approach, combining the Lebeau--Robbiano strategy with the moment method, to establish constructive null controllability for the KdV equation. This approach is then coupled with precise spectral analysis and invariant manifold theory to characterize the asymptotic behavior of the decay rate as the length of the interval approaches the set of critical lengths. Building on our classification of the critical lengths, we show that the KdV equation exhibits distinct asymptotic behaviors in neighborhoods of different types of critical lengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability of a Korteweg--de Vries equation close to critical lengths Niu, Jingrui Xiang, Shengquan Analysis of PDEs Optimization and Control 35Q53, 93C20, 93D23 In this paper, we investigate the quantitative exponential stability of the Korteweg-de Vries equation on a finite interval with its length close to the critical set. Sharp decay estimates are obtained via a constructive PDE control framework. We first introduce a novel transition-stabilization approach, combining the Lebeau--Robbiano strategy with the moment method, to establish constructive null controllability for the KdV equation. This approach is then coupled with precise spectral analysis and invariant manifold theory to characterize the asymptotic behavior of the decay rate as the length of the interval approaches the set of critical lengths. Building on our classification of the critical lengths, we show that the KdV equation exhibits distinct asymptotic behaviors in neighborhoods of different types of critical lengths. |
| title | Stability of a Korteweg--de Vries equation close to critical lengths |
| topic | Analysis of PDEs Optimization and Control 35Q53, 93C20, 93D23 |
| url | https://arxiv.org/abs/2603.27605 |