{
  "abstract": "A nonlinear observer is designed for a one-dimensional quasilinear diffusion equation with Neumann boundary conditions, using as an output the state at one end of the spatial domain. The observer consists of a copy of the system, with a nonlinear (in the output) correction term at the boundary. A Lyapunov-based analysis is performed to ensure global exponential stability of the zero equilibrium for the estimation error dynamics in the $L^1$ norm. The result holds for a general nonlinear diffusivity, under the assumption that it is lower-bounded by a positive constant, i.e., that the diffusion equation is uniformly parabolic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06546",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohamed Camil Belhadjoudja"
    },
    {
      "name": "Kirsten Morris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yg9z2pba6pkm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06546",
  "fulltext_url": null,
  "id": "9yg9z2pba6pkm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06546",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
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      "arxiv",
      "math.AP"
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      "openalex",
      "2207|Stability and Controllability of Differential Equations"
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  "openalex": "W7220719216",
  "pdf_url": "https://arxiv.org/pdf/2610.06546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yg9z2pba6pkm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global $L^1$ Exponential Observer for the Quasilinear Diffusion Equation",
  "title_text": "Global L^1 Exponential Observer for the Quasilinear Diffusion Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/9yg9z2pba6pkm",
  "venue": "arXiv",
  "versions": []
}