{
  "abstract": "We design a boundary feedback for the level of the sediment bed of a continuous settler and prove that it exponentially stabilizes the linearized closed loop under a small-gain condition. The unit is modeled by a 2 x 2 system of balance laws in which the bed surface, the interface, is not a smooth part of the solution but a moving shock between a weakly hyperbolic free-settling zone and a strictly hyperbolic compression zone. We describe it by the Rankine-Hugoniot relations and map the problem onto a fixed domain. Moreover, we prove local well-posedness with a continuation criterion given by a single margin function. Then we linearize the system near an equilibrium. The linearization couples a dissipative distributed layer to one scalar, the interface position, whose equation does not contain the control. We solve this by infinitedimensional forwarding: a Sylvester kernel cancels the interface trace and isolates the interface pole, and a proportional feedback then sets its decay rate. Every hypothesis is verified on an illustrative example, a laboratory-scale continuous settler containing a bed of compact polystyrene beads.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41632",
  "author_total": 4,
  "authors": [
    {
      "name": "Mohand Ouidir Amirat"
    },
    {
      "name": "Vincent Andrieu"
    },
    {
      "name": "Mathieu Bajodek"
    },
    {
      "name": "Claire Valentin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dp2h8n6v5agpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41632",
  "fulltext_url": null,
  "id": "dp2h8n6v5agpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41632",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dp2h8n6v5agpr.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41632"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Boundary stabilization of a moving interface in a 2 x 2 weakly hyperbolic system of balance laws: application to continuous sedimentation",
  "title_text": "Boundary stabilization of a moving interface in a 2 x 2 weakly hyperbolic system of balance laws: application to continuous sedimentation",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/dp2h8n6v5agpr",
  "venue": "arXiv",
  "versions": []
}