{
  "abstract": "We investigate the global existence and energy decay properties of a weakly coupled evolution system consisting of two wave equations in a bounded domain. The system exhibits a unique structural asymmetry: a nonlinear logarithmic damping term acts exclusively as a friction-like feedback mechanism on the first wave equation, while the second equation remains completely undamped and relies solely on linear cross-coupling to transfer and dissipate its energy. We establish two primary objectives. First, by utilizing the Faedo-Galerkin approximation scheme in conjunction with the structural monotonicity properties of the non-Lipschitz logarithmic nonlinearity, we prove a rigorous global existence result for strong solutions. Second, we provide a rigorous mathematical proof demonstrating the stability and asymptotic energy decay of the solutions under suitable constraints on the cross-coupling parameter. These results provide new insights into the stabilization mechanisms of coupled hyperbolic systems under degenerate nonlinear damping.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05268",
  "author_total": 2,
  "authors": [
    {
      "name": "Salim A. Messaoudi"
    },
    {
      "name": "Suleyman Ulusoy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9g8h0nbb9y8rh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05268",
  "fulltext_url": null,
  "id": "9g8h0nbb9y8rh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05268",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7220713009",
  "pdf_url": "https://arxiv.org/pdf/2610.05268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9g8h0nbb9y8rh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Global Existence and Energy Decay of a Partially Logarithmically Damped Wave System",
  "title_text": "The Global Existence and Energy Decay of a Partially Logarithmically Damped Wave System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/9g8h0nbb9y8rh",
  "venue": "arXiv",
  "versions": []
}