{
  "abstract": "We establish strong convergence in $L^2([0,T]\\times[0,1])$ of weak solutions to a class of nonlinear PDEs with Robin boundary conditions to weak solutions of the corresponding Neumann and Dirichlet problems as the boundary parameter $κ$ tends to $0$ and $\\infty$, respectively. Our approach relies on a particle system whose hydrodynamic limits yield the Robin problem for each fixed $κ>0$. An energy estimate derived from the microscopic stochastic dynamics provides the key bounds for passing to the subsequent limits $κ\\to0$ and $κ\\to\\infty$, thereby obtaining the Neumann and Dirichlet problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25543",
  "author_total": 4,
  "authors": [
    {
      "name": "Adriana Neumann"
    },
    {
      "name": "Patrícia Gonçalves"
    },
    {
      "name": "Maria Chiara Ricciuti"
    },
    {
      "name": "Oslenne Araújo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvydjv2x6cj5j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25543",
  "fulltext_url": null,
  "id": "dvydjv2x6cj5j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25543",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223033764",
  "pdf_url": "https://arxiv.org/pdf/2610.25543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvydjv2x6cj5j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.25543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Energy Estimate and Convergence of Weak Solutions of a Class of Nonlinear PDEs with Robin Boundary Conditions",
  "title_text": "Energy Estimate and Convergence of Weak Solutions of a Class of Nonlinear PDEs with Robin Boundary Conditions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dvydjv2x6cj5j",
  "venue": "arXiv",
  "versions": []
}