Optimal bounds for the cost of fast controls of a KdV system
Optimization and Control
2026-02-16 v1 Analysis of PDEs
Abstract
We study the cost of fast controls for a linearized KdV system and a nonlinear KdV system locally, using right Neumann boundary control for non-critical lengths. Since the operator associated with the linearized system is neither self-adjoint nor skew-adjoint, its (known) spectral properties are not directly amenable to the moment method, leaving optimal cost bounds an open problem. We address this difficulty by shifting attention to a related KdV system and deriving the optimal bounds from the new one.
Cite
@article{arxiv.2602.12698,
title = {Optimal bounds for the cost of fast controls of a KdV system},
author = {Hoai-Minh Nguyen},
journal= {arXiv preprint arXiv:2602.12698},
year = {2026}
}