{
  "abstract": "We prove unique continuation for the real periodic Benjamin--Bona--Mahony equation in the energy space: a solution that equals a constant on a nonempty space--time strip is that constant everywhere. In particular, Rosier's unique continuation conjecture [23] holds without any smallness or mean assumption. It even suffices to observe, at one point $x_0$ and for $t$ in an interval, the solution and the potential $ψ=(1-\\partial_x^2)^{-1}(u+u^2/2)$ of its flux: $u(x_0,t)=C$ and $ψ(x_0,t)=C+C^2/2$ imply $u\\equiv C$, and the second condition cannot be dropped when $C=-1$. The proof uses an exponentially weighted Hamiltonian of indefinite sign with a coercive dissipation identity, and it applies to every nonconstant real polynomial flux. Consequently, Rosier's stabilization results for two localized feedback laws and for a boundary feedback hold unconditionally, for arbitrary data. Stationary step profiles show that the theorem fails in $H^s$ for $0\\leq s<1/2$. We also give a generating-series proof of single-point unique continuation for the linearized equation and discuss related control results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36204",
  "author_total": 3,
  "authors": [
    {
      "name": "Roberto de A. Capistrano Filho"
    },
    {
      "name": "Victor Hugo Gonzalez Martinez"
    },
    {
      "name": "Ailton Campos do Nascimento"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tmtx6ryvq1x8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36204",
  "fulltext_url": null,
  "id": "6tmtx6ryvq1x8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36204",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214917500",
  "pdf_url": "https://arxiv.org/pdf/2609.36204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tmtx6ryvq1x8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Unique continuation for the periodic Benjamin-Bona-Mahony equation",
  "title_text": "Unique continuation for the periodic Benjamin-Bona-Mahony equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/6tmtx6ryvq1x8",
  "venue": "arXiv",
  "versions": []
}