{
  "abstract": "Nonlinear parabolic partial differential equations frequently occur in the modeling of applied phenomena. They often exhibit complicated dynamics which is organized by their associated equilibrium solutions. As a function of the involved model parameters, the equilibria can be detected using a bifurcation analysis, which in turn is centered around a deeper understanding of bifurcation points. In many applied systems establishing these organizing centers rigorously is difficult to achieve using traditional mathematical techniques. In this paper, we propose a theoretical framework for computer-assisted proofs of symmetry-induced transcritical and pitchfork bifurcations in nonlinear problems. This s accomplished by reformulating the existence question via a zero finding problem for an associated extended nonlinear system. The approach is general and allows for a wide variety of underlying symmetries. We demonstrate how these results can be applied in the setting of parabolic systems and higher-order equations, on both one- and two-dimensional domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38629",
  "author_total": 3,
  "authors": [
    {
      "name": "Maxime Breden"
    },
    {
      "name": "Evelyn Sander"
    },
    {
      "name": "Thomas Wanner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/802g6y6vyqa30.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38629",
  "fulltext_url": null,
  "id": "802g6y6vyqa30",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38629",
  "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.DS"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7215029423",
  "pdf_url": "https://arxiv.org/pdf/2609.38629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/802g6y6vyqa30.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Validation of Symmetry Induced Bifurcation Points in Nonlinear Diffusion Problems",
  "title_text": "Validation of Symmetry Induced Bifurcation Points in Nonlinear Diffusion Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/802g6y6vyqa30",
  "venue": "arXiv",
  "versions": []
}