{
  "abstract": "We develop a nonlinear continuum transport model for localized traveling structures in a coupled two-phase medium. The model is derived from an Einstein-type material-balance formulation combining diffusion with directed transport induced by the relative gradient of an evolving background phase. The resulting system couples diffusion, nonlinear gradient-driven transport, and irreversible background depletion. The framework provides a mathematical model for chemotactic transport and a possible modeling perspective for processes associated with the formation of oil and gas deposits. We analyze traveling-wave solutions and identify beta = chi/D = 1 as the critical threshold for globally positive localized traveling bands under prescribed asymptotic conditions as the traveling coordinate s tends to plus or minus infinity. Such bands exist for beta greater than or equal to 1, whereas for 0 < beta < 1 the positive branch reaches zero background concentration at a finite traveling coordinate. For beta greater than or equal to 1, explicit profiles are obtained and, for fixed wave speed c > 0 and right-end state V_plus > 0, are unique up to spatial translation in the traveling coordinate s. We further derive the variable-coefficient linearized perturbation operator and establish a conditional finite-time a priori estimate for the mobile-phase perturbation under bounded background forcing using a maximum-principle argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.04177",
  "author_total": 2,
  "authors": [
    {
      "name": "Isanka Garli Hevage"
    },
    {
      "name": "Akif Ibragimov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nw9z5xqyzhyf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.04177",
  "fulltext_url": null,
  "id": "6nw9z5xqyzhyf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.04177",
  "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"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7196946663",
  "pdf_url": "https://arxiv.org/pdf/2608.04177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nw9z5xqyzhyf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2608.04177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.04177"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Traveling-Wave Solutions for an Einstein-Type Material-Balance Model of the Chemotactic Transport",
  "title_text": "Traveling-Wave Solutions for an Einstein-Type Material-Balance Model of the Chemotactic Transport",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/6nw9z5xqyzhyf",
  "venue": "arXiv",
  "versions": []
}