{
  "abstract": "This article studies the ϕ(h)-null controllability of a space-discrete approximation of the linear Korteweg-de Vries (KdV) equation posed on a bounded domain, with a localized interior control. The notion of ϕ(h)-null controllability is a suitable analogue of null controllability in the context of discretized control systems. We employ a duality approach, reducing the controllability problem to an observability inequality for the associated discrete adjoint system. To this end, we first establish a suitable discrete Carleman estimate for the underlying discrete dispersive operator with a localized observation term. As a consequence, we derive a relaxed observability inequality, which allows us to establish the ϕ(h)-null controllability of the space-discrete control system. Furthermore, we show that the controls obtained for the discrete system converge, as h tends to 0, to a control driving the associated continuous KdV control system to zero, thereby recovering the null controllability of the continuous system as well.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Manish Kumar"
    },
    {
      "name": "Rajib Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ne5a62k1yjbm.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4ne5a62k1yjbm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05768404v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-oc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05768404/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ne5a62k1yjbm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:42Z",
      "native_id": "hal-05768404",
      "source": "hal",
      "url": "https://hal.science/hal-05768404v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "ϕ-Null controllability of a semi-discrete linear KdV equation with localized interior control",
  "title_text": "ϕ-Null controllability of a semi-discrete linear KdV equation with localized interior control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:42Z",
  "url": "https://research.draconitic.com/paper/4ne5a62k1yjbm",
  "venue": "HAL",
  "versions": []
}