{
  "abstract": "We investigate the optimal damping design and exponential stabilization for a class of higher-dimensional weakly degenerate damped wave equations. In weighted Sobolev spaces, we establish well-posedness and uniform exponential energy decay, and verify the existence of long-time optimal damping potentials. To overcome analytical difficulties arising from system non-self-adjointness, we use finite-time approximation via semigroup operator norms. Through linearization and adjoint-state analysis, we derive first-order necessary optimality conditions and show finite-time optimal dampings possess a bang-bang structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27502",
  "author_total": 4,
  "authors": [
    {
      "name": "Mengze Gu"
    },
    {
      "name": "Dong-Hui Yang"
    },
    {
      "name": "Hongli Sun"
    },
    {
      "name": "Yuanzhi Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83rpfek05c7gk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27502",
  "fulltext_url": null,
  "id": "83rpfek05c7gk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27502",
  "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.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214156992",
  "pdf_url": "https://arxiv.org/pdf/2609.27502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83rpfek05c7gk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal damping design and exponential stabilization for weakly degenerate wave equations",
  "title_text": "Optimal damping design and exponential stabilization for weakly degenerate wave equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/83rpfek05c7gk",
  "venue": "arXiv",
  "versions": []
}