{
  "abstract": "We study a one-dimensional reaction-diffusion and advection-reaction-diffusion system arising from a heterogeneous glioblastoma model with shared crowding effects. The two components represent latent subpopulation densities that both diffuse and proliferate; the second is additionally subject to a constant advective bias, with crowding coupled through the total density. On a bounded interval, under either componentwise Neumann conditions or the natural zero-flux condition for the advective component, we establish a global well-posedness theory, positivity preservation, invariant regions, and uniform absorbing bounds in the supremum norm. Under the zero-flux condition, the invariant and absorbing upper barriers for the second component carry the exponential spatial weight \\(e^{(a/ D_v)x}\\), in contrast to the constant barriers available under componentwise Neumann conditions. We further formulate the associated semiflow and prove the existence of a global attractor.",
  "abstract_shown": true,
  "affiliations": [
    "Yunnan Normal Univ., Kunming, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Zhipeng Yang"
    },
    {
      "affs": [
        0
      ],
      "name": "Zhenyu Zhan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfbm2g0n8kt6j.bib",
  "cited_by": 0,
  "doi": "10.58997/ejde.2026.68",
  "fulltext_url": "http://ejde.math.txstate.edu/Volumes/2026/68/abstr.html",
  "id": "bfbm2g0n8kt6j",
  "issns": [
    "1072-6691"
  ],
  "landing_url": "http://ejde.math.txstate.edu/Volumes/2026/68/abstr.html",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7213235528",
  "pdf_url": "https://ejde-ojs-txstate.tdl.org/ejde/article/download/2555/832",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "Texas State University",
  "ris": "https://research.draconitic.com/paper/bfbm2g0n8kt6j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:05Z",
      "native_id": "45fcc59af0544a9981f1edd4306f36fd",
      "source": "doaj",
      "url": "http://ejde.math.txstate.edu/Volumes/2026/68/abstr.html"
    },
    {
      "first_seen": "2026-10-31T14:21:44Z",
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      "source": "doaj",
      "url": "https://doi.org/10.58997/ejde.2026.68"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2611|Mathematical Biology Tumor Growth",
      "subfield": "general"
    }
  ],
  "title": "Global well-posedness and invariant regions for a one-dimensional RD-ARD glioblastoma model",
  "title_text": "Global well-posedness and invariant regions for a one-dimensional RD-ARD glioblastoma model",
  "type": "peer-reviewed",
  "updated_at": "2026-10-31T14:21:44Z",
  "url": "https://research.draconitic.com/paper/bfbm2g0n8kt6j",
  "venue": "Electronic Journal of Differential Equations",
  "versions": []
}