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arXiv · 2602.12698

Optimal bounds for the cost of fast controls of a KdV system

Hoai-Minh Nguyen
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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.

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Hoai-Minh Nguyen. 2026-02-13. Optimal bounds for the cost of fast controls of a KdV system. https://arxiv.org/abs/2602.12698

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